qu.1.topic=Pooled SD  Simple df@

qu.1.1.mode=Multiple Choice@
qu.1.1.name=09. Birthweight@
qu.1.1.comment=@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$Q="09";
$n1=range(30,50);
$N1=range(100,150,1);
$n2=range(20,30);
$N2=range(100,140);
$P1=$n1/$N1;
$P2=$n2/$N2;
$SE=sqrt(($P1*(1-$P1)/$N1)+($P2*(1-$P2)/$N2));
$P=$P1-$P2;
$ANS1=decimal(3,$P-1.96*$SE);
$ANS2=decimal(3,$P+1.96*$SE);
$ALT11=$ANS1-range(0.1,0.5,0.01);
$ALT12=$ANS1+range(0.1,0.5,0.01);
$ALT21=$ANS1-range(0.1,0.5,0.01);
$ALT22=$ANS1+range(0.1,0.5,0.01);
$ALT31=$ANS1-range(0.1,0.5,0.01);
$ALT32=$ANS1+range(0.1,0.5,0.01);@
qu.1.1.uid=082dac1e-2657-4c4b-9964-c82a48259259@
qu.1.1.info=  Type=MC;
  Course=202;
@
qu.1.1.question=<div title="UW Statistics Bank/Confidence Intervals/Pooled SD, Simple df/Q$Q">The number of infants with low birthweight (2500 g or less) born with the mother under a bed rest regimen versus a control group are shown in the table:&nbsp;
<div align="center"><center>
<table cellspacing="0" cellpadding="3" bordercolor="#111111" border="1" id="AutoNumber1" style="border-collapse: collapse">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td>Bed Rest</td>
            <td>Controls</td>
        </tr>
        <tr>
            <td>Low birth weight</td>
            <td>$n1</td>
            <td>$n2</td>
        </tr>
        <tr>
            <td>Total</td>
            <td>$N1</td>
            <td>$N2</td>
        </tr>
    </tbody>
</table>
</center></div>
<p>Let p1 and p2 represent the probability of a low-birthweight baby in the two conditions. Construct a 95% confidence interval for (p1-p2).</p>
</div>@
qu.1.1.answer=1@
qu.1.1.choice.1=($ANS1 , $ANS2)@
qu.1.1.choice.2=($ALT11 , $ALT12)@
qu.1.1.choice.3=($ALT21 , $ALT22)@
qu.1.1.choice.4=($ALT31, $ALT32)@
qu.1.1.fixed=@

qu.1.2.mode=Multiple Choice@
qu.1.2.name=04. Cereal@
qu.1.2.comment=@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$Q=4;
$Which=rint(4);
$Align=switch(rint(2),"Left","Right");
$U1=range(14,15,0.1);
$U2=range(10,13,0.01);
$N1=range(7,11,1);
$N2=range(8,12,1);
$S1=range(1,3,0.1);
$S2=range(1,3,0.01);
$S=sqrt((($S1^2)*($N1-1)+($S2^2)*($N2-1))/($N1+$N2-2));
$DF=$N1+$N2-2;
$T=maple("stats[statevalf,icdf,studentst[$DF]](0.975)");
$U=$U1-$U2;
$SE=decimal(3,$T*$S/sqrt($N1+$N2));
$ALT11=$U+range(0.01,0.05,0.001)-($SE+range(0.5,1.0,0.01));
$ALT12=$U+range(0.01,0.05,0.001)+($SE+range(0.5,1.0,0.01));
$ALT21=$U-($SE-range(0.5,1.0,0.01));
$ALT22=$U+($SE-range(0.5,1.0,0.01));
$ALT31=$U-($SE+range(0.5,1.0,0.01));
$ALT32=$U+($SE+range(0.5,1.0,0.01));
$ANS1=$U-$SE;
$ANS2=$U+$SE;@
qu.1.2.uid=8ffd9480-c60d-425d-b0d5-d4d066f625c6@
qu.1.2.info=  Course=202;
@
qu.1.2.question=<div title="UW Statistics Bank/Confidence Intervals/Pooled SD, Simple df/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:calculator.gif]" /></a><img hspace="4" align="$Align" src="__BASE_URI__CI/PooledSD_Simpledf/Cereal$Which.gif" title="Cereal [IMG:Cereal$Which.gif]" alt="Cereal" />Popular wisdom is that eating pre-sweetened cereal tends to increase the number of dental caries (cavities) in children. A sample of children was (with parental consent) entered into a study and followed for several years. Each child was classified as a sweetened-cereal lover or a non-sweetened cereal lover. At the end of the study, the amount of tooth damage was measured. Here is the summary data:
<p>&nbsp;</p>
<div align="center"><center>
<table cellspacing="1" cellpadding="3" border="1" id="AutoNumber1">
    <tbody>
        <tr>
            <td><strong>Group</strong></td>
            <td align="center"><strong>n</strong></td>
            <td align="center"><strong>mean</strong></td>
            <td align="center"><strong>std. dev</strong></td>
        </tr>
        <tr>
            <td><strong>Sugar Bombed</strong></td>
            <td align="center">$N1</td>
            <td align="center">$U1</td>
            <td align="center">$S1</td>
        </tr>
        <tr>
            <td><strong>No sugar</strong></td>
            <td align="center">$N2</td>
            <td align="center">$U2</td>
            <td align="center">$S2</td>
        </tr>
    </tbody>
</table>
</center></div>
<p>An approximate 95% confidence interval for the difference in the mean tooth damage is:</p>
</div>@
qu.1.2.answer=1@
qu.1.2.choice.1=($ANS1 , $ANS2)@
qu.1.2.choice.2=($ALT11 , $ALT12)@
qu.1.2.choice.3=($ALT21 , $ALT22)@
qu.1.2.choice.4=($ALT31 , $ALT32)@
qu.1.2.fixed=@

qu.1.3.mode=Multiple Choice@
qu.1.3.name=08. Penguins in North Pole@
qu.1.3.comment=@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$Q=8;
$U1=range(14,15,0.1);
$U2=range(10,13,0.01);
$N1=range(15,35,1);
$N2=range(18,42,1);
$S1=range(1,3,0.1);
$S2=range(1,3,0.01);
$S=sqrt((($S1^2)*($N1-1)+($S2^2)*($N2-1))/($N1+$N2-2));
$DF=$N1+$N2-2;
$T=maple("stats[statevalf,icdf,studentst[$DF]](0.995)");
$U=$U1-$U2;
$SE=decimal(3,$T*$S/sqrt($N1+$N2));
$ALT11=$U+range(0.01,0.05,0.001)-($SE+range(0.5,1.0,0.01));
$ALT12=$U+range(0.01,0.05,0.001)+($SE+range(0.5,1.0,0.01));
$ALT21=$U-($SE-range(0.5,1.0,0.01));
$ALT22=$U+($SE-range(0.5,1.0,0.01));
$ALT31=$U-($SE+range(0.5,1.0,0.01));
$ALT32=$U+($SE+range(0.5,1.0,0.01));
$ANS1=$U-$SE;
$ANS2=$U+$SE;@
qu.1.3.uid=2edea9f8-ef3a-4795-b1ca-0fced5f1ef06@
qu.1.3.info=  Course=202;
@
qu.1.3.question=<div title="UW Statistics Bank/Confidence Intervals/Pooled SD, Simple df/Q$Q">Suppose you are to compare the average weight of penguins at 2 locations in Antartica . You collected samples from each location and compare their means and variances. The data are given below.<br />
<br />
<table cellspacing="1" cellpadding="3" border="0" id="AutoNumber1">
    <tbody>
        <tr>
            <td><strong>Group</strong></td>
            <td align="center"><strong>n</strong></td>
            <td align="center"><strong>mean (kg)<br />
            </strong></td>
            <td align="center"><strong>std. dev</strong></td>
        </tr>
        <tr>
            <td><strong>Location 1</strong></td>
            <td align="center">$N1</td>
            <td align="center">$U1</td>
            <td align="center">$S1</td>
        </tr>
        <tr>
            <td><strong>Location 2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </strong></td>
            <td align="center">$N2</td>
            <td align="center">$U2</td>
            <td align="center">$S2</td>
        </tr>
    </tbody>
</table>
<p>&nbsp;Calculate the 99% confidence interval&nbsp;of the difference between the means.</p>
<p>&nbsp;</p>
</div>@
qu.1.3.answer=2@
qu.1.3.choice.1=($ALT11 , $ALT12)@
qu.1.3.choice.2=($ANS1 , $ANS2)@
qu.1.3.choice.3=($ALT21, $ALT22)@
qu.1.3.choice.4=($ALT31, $ALT32)@
qu.1.3.fixed=@

qu.1.4.mode=Multiple Choice@
qu.1.4.name=01. Breast vs Bottle@
qu.1.4.comment=@
qu.1.4.editing=useHTML@
qu.1.4.solution=@
qu.1.4.algorithm=$Q=1;
$Which=1+rint(5);
$Align=switch(rint(2),"Left","Right");
$U1=range(14,15,0.1);
$U2=range(10,13,0.01);
$N1=range(7,11,1);
$N2=range(8,12,1);
$S1=range(1,3,0.1);
$S2=range(1,3,0.01);
$SP=sqrt((($S1^2)($N1-1)+($S2^2)($N2-1))/($N1+$N2-2));
$DF=$N1+$N2-2;
$T=maple("stats[statevalf,icdf,studentst[$DF]](0.99)");
$U=$U1-$U2;
$SE=decimal(3,$T*$SP/sqrt(($N1+$N2)));
$ALT11=$U+range(0.01,0.05,0.001);
$ALT12=$SE+range(0.5,1.0,0.01);
$ALT21=$U;
$ALT22=$SE-range(0.5,1.0,0.01);
$ALT31=$U;
$ALT32=$SE+range(0.5,1.0,0.01);@
qu.1.4.uid=007a340a-1413-4fff-8289-cd2a8157fd8d@
qu.1.4.info=  Course=202;
  Type=MC;
@
qu.1.4.question=<div title="UW Statistics Bank/Confidence Intervals/Pooled Sd, Simple df/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a><img hspace="4" align="$Align" alt="Baby" title="Baby [IMG:Baby$Which.gif]" src="__BASE_URI__CI/PooledSD_Simpledf/Baby$Which.gif" />In a study of iron deficiency among infants, random samples of infants following different feeding programs were compared. One group contained breast-fed infants, while the children in another group were fed by a standard baby formula without any iron supplements. Here are summary results of blood hemoglobin levels at 12 months of age.<br />
<div align="center"><center>
<table cellspacing="1" cellpadding="3" border="0" id="AutoNumber1">
    <tbody>
        <tr>
            <td valign="top" height="40">
            <p align="left"><font size="2" face="SFTT1000"><strong>Group&nbsp;&nbsp; </strong></font></p>
            </td>
            <td valign="top" height="40"><strong><font size="2" face="SFTT1000">Sample <br />
            Size</font></strong></td>
            <td valign="top" height="40"><strong><font size="2" face="SFTT1000">Sample <br />
            Mean</font></strong></td>
            <td valign="top" height="40"><strong><font size="2" face="SFTT1000">Sample <br />
            Std. Deviation</font></strong></td>
        </tr>
        <tr>
            <td height="19"><strong><font size="2" face="SFTT1000">Breast-fed </font></strong></td>
            <td height="19" align="center"><font size="2" face="SFTT1000">$N1&nbsp;</font></td>
            <td height="19" align="center"><font size="2" face="SFTT1000">$U1&nbsp;</font></td>
            <td height="19" align="center"><font size="2" face="SFTT1000">$S1</font></td>
        </tr>
        <tr>
            <td height="19"><strong><font size="2" face="SFTT1000">Formula-fed </font></strong></td>
            <td height="19" align="center"><font size="2" face="SFTT1000">$N2&nbsp;</font></td>
            <td height="19" align="center"><font size="2" face="SFTT1000">$U2&nbsp;</font></td>
            <td height="19" align="center"><font size="2" face="SFTT1000">$S2</font></td>
        </tr>
    </tbody>
</table>
</center></div>
<p>A 98% confidence interval for the mean difference in hemoglobin level between the two populations of infants is:</p>
</div>@
qu.1.4.answer=4@
qu.1.4.choice.1=$ALT11 ± $ALT12@
qu.1.4.choice.2=$ALT21 ± $ALT22@
qu.1.4.choice.3=$ALT31 ± $ALT32@
qu.1.4.choice.4=$U ± $SE@
qu.1.4.fixed=@

qu.2.topic=Student t@

qu.2.1.question=<div title="UW Statistics Bank/Confidence Intervals/Student t/Q$Q">A previous analysis of paper boxes showed that the the standard deviation of their lengths is $S millimeters. A packer wishes to find the $PER% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within $X millimeters?</div>@
qu.2.1.answer.num=$Ans@
qu.2.1.answer.units=@
qu.2.1.showUnits=false@
qu.2.1.grading=exact_value@
qu.2.1.negStyle=minus@
qu.2.1.numStyle=thousands scientific dollars arithmetic@
qu.2.1.mode=Numeric@
qu.2.1.name=03a. Boxes@
qu.2.1.comment=@
qu.2.1.editing=useHTML@
qu.2.1.solution=@
qu.2.1.algorithm=$Q="03a";
$X = range(3,7,1);
$S = range(7,10,1);
$PER = range(90,99,1);
$P = $PER/100;
$Z = (1-$P)/2;
$I = maple("(stats[statevalf,icdf,normald]($Z))");
$A = -$I;
$Ans = decimal(0,($A*$S/$X)*($A*$S/$X));@
qu.2.1.uid=2c6eced0-10c6-4b7b-a646-799bb787160a@
qu.2.1.info=  Course=202;
  Type=numeric;
@

qu.2.2.mode=Multiple Choice@
qu.2.2.name=02. Snacks@
qu.2.2.comment=<p>Use the formula <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>y</mi></mrow><mi>__</mi></mover></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><msub><mi>t</mi><mrow><mn>0.025</mn></mrow></msub></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mfrac><mi>s</mi><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mrow></mstyle></math> . With degrees of freedom = $DF we have t<sub>0.025</sub> = $t so our confidence interval is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$Mean</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><mi mathvariant='normal'>$t</mi><mfrac><mrow><mi mathvariant='normal'>$SD</mi></mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$LP</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>$RP</mi></mrow></mfenced></mrow></mstyle></math></p>@
qu.2.2.editing=useHTML@
qu.2.2.solution=@
qu.2.2.algorithm=$Q="02";
$Which=rint(3);
$SnackP=rint(5);
$Align=switch(rint(2),"Left","Right");
$Snack=switch($SnackP,"cookies","peanuts","popcorn","potato chips","pretzels");
$GIFName=switch($SnackP,"Cookie","Nuts","Popcorn","Chips","Pretzel");

$n=range(6,12,1);
$DF=$n-1;
$Pret=maple("stats[statevalf,icdf,studentst[$DF]](0.975)");
$t=decimal(3,$Pret);
$Mean=range(9.1,9.9,0.1);
$SD=range(0.15,0.35,0.05);
$LP=decimal(2,$Mean-$t*$SD/sqrt($n));
$RP=decimal(2,$Mean+$t*$SD/sqrt($n));
$Alt1LP=decimal(2,range(0.85,0.95,0.05)*$LP);
$Alt1RP=decimal(2,$Mean+range(0.35,0.65,0.05)*($RP-$Mean));
$Alt2LP=decimal(2,$Mean-$t*$SD/$n);
$Alt2RP=decimal(2,0.5*($RP+$Alt1RP));
$Alt3LP=decimal(2,0.5*($Alt1LP+$Alt2LP));
$Alt3RP=switch(rint(3),$RP,$Alt1RP,$Alt2RP);@
qu.2.2.uid=4d78836a-049a-43ff-aaaf-e3e653036668@
qu.2.2.info=  Type=MC;
  Course=202;
@
qu.2.2.question=<div title="UW Statistics Bank/Confidence Intervals/Student t/Q$Q"><img hspace="4" align="$Align" alt="$Snack " title="$Snack [IMG:Snack$SnackP$GIFName$Which.gif]" src="__BASE_URI__CI/Student_t/Snack$SnackP$GIFName$Which.gif" />A food snack manufacturer samples $n bags of $Snack off the assembly line and weighed their contents. If the sample mean is $Mean and the sample standard deviation is $SD, find the 95% confidence interval of the true mean.</div>@
qu.2.2.answer=4@
qu.2.2.choice.1=($Alt1LP,$Alt1RP)@
qu.2.2.choice.2=($Alt2LP, $Alt2RP)@
qu.2.2.choice.3=($Alt3LP,$Alt3RP)@
qu.2.2.choice.4=($LP, $RP)@
qu.2.2.fixed=@

qu.2.3.mode=Multiple Choice@
qu.2.3.name=04. Basketball@
qu.2.3.comment=@
qu.2.3.editing=useHTML@
qu.2.3.solution=@
qu.2.3.algorithm=$Q="04";
$n=range(6,12,1);
$DF=$n-1;
$Pret=maple("stats[statevalf,icdf,studentst[$DF]](0.99)");
$t=decimal(3,$Pret);
$Mean=range(20,35);
$SD=range(2,7);
$LP=decimal(2,$Mean-$t*$SD/sqrt($n));
$RP=decimal(2,$Mean+$t*$SD/sqrt($n));
$Alt1LP=decimal(2,range(0.85,0.95,0.05)*$LP);
$Alt1RP=decimal(2,$Mean+range(0.35,0.65,0.05)*($RP-$Mean));
$Alt2LP=decimal(2,$Mean-$t*$SD/$n);
$Alt2RP=decimal(2,0.5*($RP+$Alt1RP));
$Alt3LP=decimal(2,0.5*($Alt1LP+$Alt2LP));
$Alt3RP=switch(rint(3),$RP,$Alt1RP,$Alt2RP);@
qu.2.3.uid=4d3580dc-3303-492e-93e2-191681f74e2d@
qu.2.3.info=  Course=202;
  Type=MC;
@
qu.2.3.question=<div title="UW Statistics Bank/Confidence Intervals/Student t/Q$Q">The winning team's scores in&nbsp;$n high school basketball games were recorded. If the sample mean is&nbsp;$Mean points and the sample standard deviation is&nbsp;$SD points, find the 98% confidence interval of the true mean.</div>@
qu.2.3.answer=3@
qu.2.3.choice.1=($Alt1LP, $Alt1RP)@
qu.2.3.choice.2=($Alt2LP, $Alt2RP)@
qu.2.3.choice.3=($LP, $RP)@
qu.2.3.choice.4=($Alt3LP, $Alt3RP)@
qu.2.3.fixed=@

qu.2.4.mode=Multiple Choice@
qu.2.4.name=03b. Boxes@
qu.2.4.comment=@
qu.2.4.editing=useHTML@
qu.2.4.solution=@
qu.2.4.algorithm=$Q="03b";
$X = range(3,7,1);
$S = range(7,10,1);
$PER = range(90,99,1);
$P = $PER/100;
$Z = (1-$P)/2;
$I = maple("(stats[statevalf,icdf,normald]($Z))");
$A = -$I;
$Ans = decimal(0,($A*$S/$X)*($A*$S/$X));
$Alt1=int(range(1.1,1.9,0.01)*$Ans);
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));
condition:ne(0,($Alt3-$Alt1)*($Alt3-$Alt2));@
qu.2.4.uid=fc42643e-cd3e-445f-8be1-34d5aaf321a4@
qu.2.4.info=  Course=202;
  Type=MC;
@
qu.2.4.question=<div title="UW Statistics Bank/Confidence Intervals/Student t/Q$Q">A previous analysis of paper boxes showed that the the standard deviation of their lengths is $S millimeters. A packer wishes to find the $PER% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within $X millimeters?</div>@
qu.2.4.answer=1@
qu.2.4.choice.1=$Ans@
qu.2.4.choice.2=$Alt1@
qu.2.4.choice.3=$Alt2@
qu.2.4.choice.4=$Alt3@
qu.2.4.fixed=@

qu.2.5.mode=Multiple Choice@
qu.2.5.name=01. Accounts Receivable@
qu.2.5.comment=<p>First determine the sample mean: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$X1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$X2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$X3</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$X4</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$X5</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$U</mi></mrow></mstyle></math> and standard deviation <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>s</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$X1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$U</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$X2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$U</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$X3</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$U</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$X4</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$U</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$X5</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$U</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>5</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></mfrac></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$S</mi></mrow></mstyle></math>. The t-value for a confidence level of $CL is $T, so the interval is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$U</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mrow><mi mathvariant='normal'>$T</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$S</mi></mrow></mfenced></mrow><mrow><msqrt><mrow><mn>5</mn></mrow></msqrt></mrow></mfrac><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>$U</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mrow><mi mathvariant='normal'>$T</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$S</mi></mrow></mfenced></mrow><mrow><msqrt><mrow><mn>5</mn></mrow></msqrt></mrow></mfrac></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$Ans1</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>$Ans2</mi></mrow></mfenced></mrow></mstyle></math></p>@
qu.2.5.editing=useHTML@
qu.2.5.solution=@
qu.2.5.algorithm=$Q="01";
$Who=switch(rint(2),"An accountant","An auditor","A comptroller");
$CL=0.95;
$X1=range(30,40,0.1);
$X2=range(30,40,0.1);
$X3=range(30,40,0.1);
$X4=range(30,40,0.1);
$X5=range(30,40,0.1);
$U=($X1+$X2+$X3+$X4+$X5)/5;
$V=((($X1-$U)^2)+(($X2-$U)^2)+(($X3-$U)^2)+(($X4-$U)^2)+(($X5-$U)^2))/4;
$S=sqrt($V);
$PreT=maple("stats[statevalf,icdf,studentst[4]]($CL)");
$T=decimal(4,$PreT);
$Inc=$T*$S/sqrt(5);
$Ans1=decimal(4,$U-$Inc);
$Ans2=decimal(4,$U+$Inc);
$Inc1=range(1.1,1.9,0.01)*$Inc;
$Alt11=decimal(4,$U-$Inc1);
$Alt12=decimal(4,$U+$Inc1);
$Inc2=range(0.5,0.9,0.01)*$Inc;
$Alt21=decimal(4,$U-$Inc2);
$Alt22=decimal(4,$U+$Inc2);
$Alt31=decimal(4,0.5*($Ans1+switch(rint(2),$Alt11,$Alt21)));
$Alt32=decimal(4,0.5*($Ans2+switch(rint(2),$Alt12,$Alt22)));@
qu.2.5.uid=58b57c9d-ad8d-4e20-ba1a-184a8d3b8387@
qu.2.5.info=  Course=202;
  Type=MC;
@
qu.2.5.question=<div title="UW Statistics Bank/Confidence Intervals/Student t/Q$Q">$Who is auditing a list of account receivables in a corporation. A sample of accounts were taken (in millions) :<br />
<p>&nbsp;</p>
<div align="center"><center>
<table cellspacing="0" cellpadding="3" bordercolor="#111111" border="1" style="border-collapse: collapse" id="AutoNumber1">
    <tbody>
        <tr>
            <td>Account:</td>
            <td>1</td>
            <td>2</td>
            <td>3</td>
            <td>4</td>
            <td>5</td>
        </tr>
        <tr>
            <td>\\$Millions:</td>
            <td>$X1</td>
            <td>$X2</td>
            <td>$X3</td>
            <td>$X4</td>
            <td>$X5</td>
        </tr>
    </tbody>
</table>
</center></div>
<p><br />
Contruct a 90% confidence interval for the&nbsp;sample mean</p>
</div>@
qu.2.5.answer=1@
qu.2.5.choice.1=($Ans1, $Ans2)@
qu.2.5.choice.2=($Alt11, $Alt12)@
qu.2.5.choice.3=($Alt21, $Alt22)@
qu.2.5.choice.4=($Alt31, $Alt32)@
qu.2.5.fixed=@

qu.3.topic=Normal (Mean)@

qu.3.1.question=<div title="UW Statistics Bank/Confidence Intervals/Basics/Q$Q"><img hspace="4" align="$Align" src="__BASE_URI__CI/Normal_Mean/AgPlant$Pick.gif" alt="$Plant" title="$Plant [IMG:AgPlant$Pick.gif]" />An agronomist measured the height of $n $Plant plants. The mean height was $U&nbsp;cm and the standard deviation was $s cm. Calculate the standard error of the mean. (3 decimal accuracy)</div>@
qu.3.1.answer.num=$Ans@
qu.3.1.answer.units=@
qu.3.1.showUnits=false@
qu.3.1.grading=toler_abs@
qu.3.1.err=0.01@
qu.3.1.negStyle=minus@
qu.3.1.numStyle=thousands scientific dollars arithmetic@
qu.3.1.mode=Numeric@
qu.3.1.name=01a. SE: Ag Plant Height@
qu.3.1.comment=<p>The Standard Error is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mi>s</mi><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$s</mi><mrow><msqrt><mrow><mi mathvariant='normal'>$n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math>, where <em>s</em> is sample SD.</p>
<p>Notice that the sample mean does not matter for this result!</p>@
qu.3.1.editing=useHTML@
qu.3.1.solution=@
qu.3.1.algorithm=$Q="1a";
$Pick=rint(4);
$Plant=switch($Pick,"Wheat","Corn","Soybean","Canola");
$Align=switch(rint(2),"Left","Right");
$U=range(200,250,1);
$s=range(10,20,1);
$n=range(100,150,1);
$Ans = decimal(4,$s/sqrt($n));@
qu.3.1.uid=6d598fd7-4ae8-41da-b324-6c4b30f2868a@
qu.3.1.info=  Course=202;
  Type=numeric;
@

qu.3.2.mode=Multiple Choice@
qu.3.2.name=05. Animal weights of a group@
qu.3.2.comment=<p>For a $PER% CI we need to find z such that $SayZ% of the standard normal curve area lies to the left of <font size="3" face="Times New Roman"><em>z</em></font>. This value is <font size="3" face="Times New Roman"><em>z</em> = $A</font>. Since the CI is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;</mi><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><mfrac><mrow><mi>z</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>SD</mi></mrow><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mstyle></math> we need to find <font size="3" face="Times New Roman"><em>n</em></font> such that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mi>z</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>SD</mi></mrow><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&simeq;</mo><mi>$X</mi></mrow></mstyle></math>. Solving: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>$S</mi></mrow><mrow><mi mathvariant='normal'>$X</mi></mrow></mfrac></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&simeq;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math></p>@
qu.3.2.editing=useHTML@
qu.3.2.solution=@
qu.3.2.algorithm=$Q="05";
$X = range(300,350,1);
$S = range(2000,2100,1);
$PER = range(90,99,1);
$P = $PER/100;
$Z = (1-$P)/2;
$SayZ=(100+$PER)/2;
$I = maple("(stats[statevalf,icdf,normald]($Z))");
$A = decimal(4,-$I);
$Ans = int(($A*$S/$X)*($A*$S/$X));
$Alt1=int(range(1.1,1.9,0.01)*$Ans);
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));
$Animal=switch(rint(3),"elephants","hippos","rhinos");
$Subgroup=switch(rint(3),"subspecies","family group","game reserve population");@
qu.3.2.uid=47f1cd35-b82f-4954-8cdb-bb36fe99d8bc@
qu.3.2.info=  Course=202;
  Type=MC;
@
qu.3.2.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Mean)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>A study of $Animal wishes to determine the average weight of a certain $Subgroup of $Animal. The standard deviation of the population is $S kilograms. How many $Animal need to be weighed so we can be $PER% confident to be accurate within $X kilograms?</div>@
qu.3.2.answer=1@
qu.3.2.choice.1=$Ans@
qu.3.2.choice.2=$Alt1@
qu.3.2.choice.3=$Alt2@
qu.3.2.choice.4=$Alt3@
qu.3.2.fixed=@

qu.3.3.mode=Multiple Choice@
qu.3.3.name=02. Stock Portfolio@
qu.3.3.comment=<p>Here we use the provided Normal calculator to get F(0.95) = 1.6449, so the 90% CI is:</p>
<p>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;</mi><mo lspace='0.0em' rspace='0.0em'>&plusmn;</mo><mfrac><mrow><mi>F</mi><mfenced open='(' close=')' separators=','><mrow><mn mathvariant='italic'>0.95</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>s</mi></mrow><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$U</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&pm;</mo><mfrac><mrow><mn>1.6449</mn><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>$S</mi></mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$N</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$U</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><mi mathvariant='normal'>$PartAns</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>or</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$ANS1</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>$ANS2</mi></mrow></mfenced></mrow></mstyle></math></p>@
qu.3.3.editing=useHTML@
qu.3.3.solution=@
qu.3.3.algorithm=$Q=2;
$U=range(1,2,0.01);
$S=range(0.1,0.2,0.01);
$N=range(40,50,1);
$DF=$N-1;
$T=maple("stats[statevalf,icdf,studentst[$DF]](0.95)");
$PartAns=1.64485*$S/sqrt($N);
$ANS1=decimal(3,$U-$PartAns);
$ANS2=decimal(3,$U+$PartAns);
$Alt1P=range(1.4,2.6,0.05)*$PartAns;
$Alt11=decimal(3,$U-$Alt1P);
$Alt12=decimal(3,$U+$Alt1P);
$Alt2P=range(0.4,0.7,0.05)*$PartAns;
$Alt21=decimal(3,$U-$Alt2P);
$Alt22=decimal(3,$U+$Alt2P);
$Alt31=$ANS1;
$Alt32=$Alt12;
$Alt41=$Alt21;
$Alt42=$ANS2;@
qu.3.3.uid=299ad452-48d8-4567-aee5-b2351ab47410@
qu.3.3.info=  Course=202;
  Type=MC;
@
qu.3.3.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Mean)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a>In an stock portfolio selection process, a financial consultant observed the value of $N stocks listed in the NASDAQ. The mean value of the stocks are USD $U (in millions) and the standard deviation is USD $S (millions). Assuming normality, a 90% confidence interval is:</div>@
qu.3.3.answer=1@
qu.3.3.choice.1=($ANS1 , $ANS2)@
qu.3.3.choice.2=($Alt11 , $Alt12)@
qu.3.3.choice.3=($Alt21 , $Alt22)@
qu.3.3.choice.4=($Alt31 , $Alt32)@
qu.3.3.choice.5=($Alt41, $Alt42)@
qu.3.3.fixed=@

qu.3.4.mode=Multiple Choice@
qu.3.4.name=01b. SE: Ag Plant Height@
qu.3.4.comment=<p>The Standard Error is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mi>s</mi><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$s</mi><mrow><msqrt><mrow><mi mathvariant='normal'>$n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math>, where <em>s</em> is sample SD.</p>
<p>Notice that the sample mean does not matter for this result!</p>@
qu.3.4.editing=useHTML@
qu.3.4.solution=@
qu.3.4.algorithm=$Q="1b";
$Pick=rint(4);
$Plant=switch($Pick,"Wheat","Corn","Soybean","Canola");
$Align=switch(rint(2),"Left","Right");
$U=range(200,250,1);
$s=range(10,20,1);
$n=range(100,150,1);
$Ans = decimal(4,$s/sqrt($n));
$Alt1=decimal(4,range(1.1,1.9,0.01)*$Ans);
$Alt2=decimal(4,range(0.5,0.9,0.01)*$Ans);
$Alt3=decimal(4,0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));@
qu.3.4.uid=f476edff-bd31-4a76-b234-b2cc34ca724d@
qu.3.4.info=  Course=202;
  Type=MC;
@
qu.3.4.question=<div title="UW Statistics Bank/Confidence Intervals/Basics/Q$Q"><img hspace="4" align="$Align" title="$Plant [IMG:AgPlant$Pick.gif]" alt="$Plant" src="__BASE_URI__CI/Normal_Mean/AgPlant$Pick.gif" />An agronomist measured the height of $n $Plant plants. The mean height was $U&nbsp;cm and the standard deviation was $s cm. Calculate the standard error of the mean.</div>@
qu.3.4.answer=1@
qu.3.4.choice.1=$Ans@
qu.3.4.choice.2=$Alt1@
qu.3.4.choice.3=$Alt2@
qu.3.4.choice.4=$Alt3@
qu.3.4.fixed=@

qu.3.5.mode=Multiple Choice@
qu.3.5.name=08. Packing object lengths@
qu.3.5.comment=<p>The z value corresponding to this confidence level is $A. We need n such that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mi>z</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>SD</mi></mrow><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&simeq;</mo><mi>$X</mi></mrow></mstyle></math> Solving: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&simeq;</mo><mrow><msup><mfenced open='[' close=']' separators=','><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$A</mi></mrow></mfenced><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$S</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$X</mi></mrow></mfrac></mfenced><mrow><mn>2</mn></mrow></msup></mrow></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math></p>@
qu.3.5.editing=useHTML@
qu.3.5.solution=@
qu.3.5.algorithm=$Q="08";
$Objects=switch(rint(3),"paper boxes","cam shafts","celery stalks");
$Packer=switch(rint(3),"packer","pallet manufacturer","bag manufacturer");
$X = range(3,7,1);
$S = range(7,10,1);
$PER = range(90,99,1);
$P = $PER/100;
$Z = (1-$P)/2;
$I = maple("(stats[statevalf,icdf,normald]($Z))");
$A = decimal(4,-$I);
$Ans = int(0.5+($A*$S/$X)*($A*$S/$X));
$Alt1=int(range(1.1,1.9,0.01)*$Ans);
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));@
qu.3.5.uid=60173339-af6f-435d-9cb2-262eaa2ed793@
qu.3.5.info=  Type=MC;
  Course=202;
@
qu.3.5.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Mean)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:calculator.gif]" /></a>A previous analysis of $Objects showed that the the standard deviation of their lengths is $S millimeters. A $Packer wishes to find the $PER% confidence interval for the average length of $Objects. How many $Objects must be measured to be accurate within &plusmn;$X millimeters?</div>@
qu.3.5.answer=1@
qu.3.5.choice.1=$Ans@
qu.3.5.choice.2=$Alt1@
qu.3.5.choice.3=$Alt2@
qu.3.5.choice.4=$Alt3@
qu.3.5.fixed=@

qu.3.6.mode=Multiple Choice@
qu.3.6.name=07. Squirrels' weights@
qu.3.6.comment=<p>Use the formula&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>y</mi></mrow><mi>_</mi></mover></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><msub><mi>t</mi><mrow><mn>0.025</mn></mrow></msub></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mfrac><mi>s</mi><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mrow></mstyle></math> . With degrees of freedom = $DF we have t<sub>0.025</sub> = $t so our confidence interval is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$Mean</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><mi mathvariant='normal'>$t</mi><mfrac><mrow><mi mathvariant='normal'>$SD</mi></mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$LP</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>$RP</mi></mrow></mfenced></mrow></mstyle></math></p>@
qu.3.6.editing=useHTML@
qu.3.6.solution=@
qu.3.6.algorithm=$Q="07";
$n=range(6,12,1);
$DF=$n-1;
$Pret=maple("stats[statevalf,icdf,studentst[$DF]](0.975)");
$t=decimal(3,$Pret);
$Mean=range(250,500,10);
$SD=range(4.15,7.35,0.05);
$LP=decimal(2,$Mean-$t*$SD/sqrt($n));
$RP=decimal(2,$Mean+$t*$SD/sqrt($n));
$Alt1LP=decimal(2,range(0.85,0.95,0.05)*$LP);
$Alt1RP=decimal(2,$Mean+range(0.35,0.65,0.05)*($RP-$Mean));
$Alt2LP=decimal(2,$Mean-$t*$SD/$n);
$Alt2RP=decimal(2,0.5*($RP+$Alt1RP));
$Alt3LP=decimal(2,0.5*($Alt1LP+$Alt2LP));
$Alt3RP=switch(rint(3),$RP,$Alt1RP,$Alt2RP);
$Which=rint(4);
$Align=switch(rint(2),"Left","Right");@
qu.3.6.uid=55c869e0-e6e9-4c5e-8cec-3bc472c8e9f4@
qu.3.6.info=  Type=MC;
  Course=202;
@
qu.3.6.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Mean)/Q$Q"><img title="Squirrel [IMG:Squirrel$Which.gif]" alt="Squirrel" src="__BASE_URI__CI/Normal_Mean/Squirrel$Which.gif" /> <a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a> $n squirrels were found to have an average weight of $Mean grams with a sample standard deviation of $SD. Find the 95% confidence interval of the true mean weight&nbsp; (assume the t-student distribution).</div>@
qu.3.6.answer=1@
qu.3.6.choice.1=($LP,$RP)@
qu.3.6.choice.2=($Alt1LP, $Alt1RP)@
qu.3.6.choice.3=($Alt2LP, $Alt2RP)@
qu.3.6.choice.4=($Alt3LP, $Alt3RP)@
qu.3.6.fixed=@

qu.3.7.mode=Multiple Choice@
qu.3.7.name=06. Carpet@
qu.3.7.comment=<p>For a $PER% CI we need to find the z value for the standard normal for which $SayZ% of the graph area lies to the left. This is $P . The CI is: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;</mi><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><mfrac><mrow><mi>z</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>SD</mi></mrow><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$X</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><mfrac><mrow><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$P</mi></mrow></mfenced><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$S</mi></mrow></mfenced></mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$N</mi></mrow></msqrt></mrow></mfrac></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$Ans1</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>$Ans2</mi></mrow></mfenced></mrow></mstyle></math></p>@
qu.3.7.editing=useHTML@
qu.3.7.solution=@
qu.3.7.algorithm=$Q="06";
$X = range(180,185,1);
$N = range(90,95);
$S = range(10,15);
$PER = range(95,99,1);
$A = $PER/100;
$Z =(1-$A)/2;
$SayZ=(100+$PER)/2;
$I = maple("(stats[statevalf,icdf,normald]($Z))");
$P=decimal(4,-$I);
$Ans1 = decimal(2,$X-$P*$S/sqrt($N));
$Ans2 = decimal(2,$X+$P*$S/sqrt($N));
$Alt11=decimal(2,range(1.1,1.9,0.01)*$Ans1);
$Alt12=decimal(2,range(1.1,1.9,0.01)*$Ans2);
condition:lt($Alt11,$Alt12);
$Alt21=decimal(2,range(0.5,0.9,0.01)*$Ans1);
$Alt22=decimal(2,range(0.5,0.9,0.01)*$Ans2);
condition:lt($Alt21,$Alt22);
$Alt31=decimal(2,0.5*($Ans1+$Alt11));
$Alt32=decimal(2,0.5*($Ans2+$Alt12));
condition:lt($Alt31,$Alt32);
$Alt41=decimal(2,0.5*($Ans1+$Alt21));
$Alt42=decimal(2,0.5*($Ans2+$Alt22));
condition:lt($Alt41,$Alt42);@
qu.3.7.uid=8a89c52b-10fe-4e40-b298-af7a2484bbb9@
qu.3.7.info=  Course=202;
  Type=MC;
@
qu.3.7.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Mean)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>A study of $N bolts of carpet showed that their average length was $X meters. The standard deviation of the population is $S m. Which of the following is the $PER% confidence interval for the mean length per bolt of carpet?</div>@
qu.3.7.answer=1@
qu.3.7.choice.1=($Ans1, $Ans2)@
qu.3.7.choice.2=($Alt21, $Alt22)@
qu.3.7.choice.3=($Alt31, $Alt32)@
qu.3.7.choice.4=($Alt11, $Alt12)@
qu.3.7.choice.5=($Alt41,$Alt42)@
qu.3.7.fixed=@

qu.3.8.mode=Multiple Choice@
qu.3.8.name=04. Judge Ages@
qu.3.8.comment=<p>To find a $PER% CI we need the value of Z such that $SayZ% of the normal curve area lies to the left of it. Use a standard normal table or the calculator provided to find this value is $P. The CI then is: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$X</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$S</mi></mrow></mfenced></mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$N</mi></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>=($Ans1, $Ans2)</p>
<p>&nbsp;</p>@
qu.3.8.editing=useHTML@
qu.3.8.solution=@
qu.3.8.algorithm=$Q="04";
$Researcher=switch(rint(3),"lawyer","public defender","clerk");
$Court=switch(rint(4),"the Supreme Court","his court","her court","the District Court");
$X = range(13,14,0.01);
$N = range(45,50,1);
$S = range(7,8,0.01);
$PER = range(95,99,1);
$A = $PER/100;
$Z =(1-$A)/2;
$SayZ=(100+$PER)/2;
$I = maple("(stats[statevalf,icdf,normald]($Z))");
$P=-$I;
$Ans1 = decimal(3,$X-$P*$S/sqrt($N));
$Ans2 = decimal(3,$X+$P*$S/sqrt($N));
$Alt11=decimal(4,range(1.1,1.9,0.01)*$Ans1);
$Alt12=decimal(4,range(1.1,1.9,0.01)*$Ans2);
condition:lt($Alt11,$Alt12);
$Alt21=decimal(4,range(0.5,0.9,0.01)*$Ans1);
$Alt22=decimal(4,range(0.5,0.9,0.01)*$Ans2);
condition:lt($Alt21,$Alt22);
$Alt31=decimal(4,0.5*($Ans1+$Alt11));
$Alt32=decimal(4,0.5*($Ans2+$Alt12));
condition:lt($Alt31,$Alt32);
$Alt41=decimal(4,0.5*($Ans1+$Alt21));
$Alt42=decimal(4,0.5*($Ans2+$Alt22));
condition:lt($Alt41,$Alt42);
$Which=rint(4);
$Align=switch(rint(2),"Left","Right");@
qu.3.8.uid=1a3fdbd7-ec65-49a6-8dde-8a4933d276c1@
qu.3.8.info=  Course=202;
  Type=MC;
@
qu.3.8.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Mean)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a><img hspace="4" align="$Align" src="__BASE_URI__CI/Normal_Mean/Judge$Which.gif" alt="Judge" title="Judge [IMG:Judge$Which.gif]" />A $Researcher researched the average number of years served by $N different judges on $Court. The average number of years served was $X years with a standard deviation of $S years. What is the $PER% confidence interval for the average number of years served by all&nbsp; such judges?</div>@
qu.3.8.answer=1@
qu.3.8.choice.1=$Ans1 < &#956; < $Ans2@
qu.3.8.choice.2=$Alt11 < &#956; < $Alt12@
qu.3.8.choice.3=$Alt21 < &#956; < $Alt22@
qu.3.8.choice.4=$Alt31 < &#956; < $Alt32@
qu.3.8.choice.5=$Alt41 < &#956; < $Alt42@
qu.3.8.fixed=@

qu.3.9.mode=Multiple Choice@
qu.3.9.name=03. SE drug test@
qu.3.9.comment=<p>Since <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi>sd</mi><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mrow></mstyle></math>we have <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mi mathvariant='normal'>$s</mi><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mrow></mstyle></math>so <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&ap;</mo><mfrac><msup><mrow><mi mathvariant='normal'>$s</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><msup><mi mathvariant='normal'>$E</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math></p>@
qu.3.9.editing=useHTML@
qu.3.9.solution=@
qu.3.9.algorithm=$Q="03";
$s=range(30,50,1);
$E=range(3,7,1);
$Ans=decimal(0,($s/$E)^2);
$Alt1=int(range(1.1,1.9,0.01)*$Ans);
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));@
qu.3.9.uid=c4b6a9a6-bbab-41dc-bae3-f0ac4e6164d6@
qu.3.9.info=  Course=202;
  Type=MC;
@
qu.3.9.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Mean)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a>A pharmacist is planning to estimate the mean level of a certain drug in a lab. The pharmacist wanted the estimate to be within <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&plusmn;</mo></mrow></mstyle></math>$E mg/dLi or less with 95% confidence.&nbsp; The pharmacist also believes that the standard deviation of the drug level is probably about $s mg/dLi. How large a sample should the pharmacist need to take?</div>@
qu.3.9.answer=1@
qu.3.9.choice.1=$Ans@
qu.3.9.choice.2=$Alt1@
qu.3.9.choice.3=$Alt2@
qu.3.9.choice.4=$Alt3@
qu.3.9.fixed=@

qu.4.topic=Normal (Proportion)@

qu.4.1.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a>A $Role wants to estimate the proportion of defective parts that are being manufactured by $Gender company to within 2.5%. A sample of $SS components showed that $NumDef were defective. How large a sample is needed to estimate the true proportion of defective parts with $Level% confidence?</div>@
qu.4.1.answer.num=$n@
qu.4.1.answer.units=@
qu.4.1.showUnits=false@
qu.4.1.grading=exact_value@
qu.4.1.negStyle=minus@
qu.4.1.numStyle=thousands scientific dollars arithmetic@
qu.4.1.mode=Numeric@
qu.4.1.name=10. Defective Components SS@
qu.4.1.comment=<p>Use the fact that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow></mstyle></math><br />
<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$Acc</mi><mrow><mn>100</mn></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$CV</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mrow><msqrt><mrow><mfrac><mfenced open='(' close=')' separators=','><mrow><mfrac><mi mathvariant='normal'>$NumDef</mi><mrow><mi mathvariant='normal'>$SS</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfrac><mrow><mi mathvariant='normal'>$SS</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$NumDef</mi></mrow><mrow><mi mathvariant='normal'>$SS</mi></mrow></mfrac></mrow></mfenced><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$CV</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mn>100</mn></mrow><mrow><mi mathvariant='normal'>$Acc</mi></mrow></mfrac></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mi mathvariant='normal'>$NumDef</mi><mrow><mi mathvariant='normal'>$SS</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfrac><mrow><mi mathvariant='normal'>$SS</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$NumDef</mi></mrow><mrow><mi mathvariant='normal'>$SS</mi></mrow></mfrac></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&cong;</mo><mi mathvariant='normal'>$n</mi></mrow></mstyle></math></p>
<p>&nbsp;</p>@
qu.4.1.editing=useHTML@
qu.4.1.solution=@
qu.4.1.algorithm=$Q="10";
$Role=switch(rint(3),"line supervisor","quality control engineer","shift manager");
$Gender=switch(rint(2),"her","his");
$L=rint(4);
$Level=switch($L,99,98,95,90);
$CV=switch($L,2.578,2.3263,1.96,1.6449);
$Acc=2.5;
$NumDef=range(5,20);
$SS=range(300,600,25);
$n=int(0.5+($CV*100/$Acc)^2*($NumDef/$SS*($SS-$NumDef)/$SS));
condition:lt($n,$SS);@
qu.4.1.uid=2d30e911-29f4-4dc3-a95b-ef0cebed12ef@
qu.4.1.info=  Type=numeric;
  Course=202;
@

qu.4.2.mode=Multiple Choice@
qu.4.2.name=08. Women shoes@
qu.4.2.comment=@
qu.4.2.editing=useHTML@
qu.4.2.solution=@
qu.4.2.algorithm=$Q="08";
$Studier=switch(rint(4),"Academy of Orthopedic Surgeons","Bata Shoe Museum","College of Podiatrists","Canadian Chiropodists Society");
$N=range(600,700,10);
$n=range(100,200,10);
$P=range(0.1,0.9,0.01);
$Z=2.326347874;
$E=range(0.01,0.05,0.01);
$Ans=int(($Z^2)*$P*(1-$P)/($E^2));
$Alt1=int(range(1.1,1.9,0.01)*$Ans);
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));
$PER=$P*100;@
qu.4.2.uid=251af06a-cb5d-480b-b6f2-fa0d7413e18c@
qu.4.2.info=  Course=202;
  Type=MC;
@
qu.4.2.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a>The $Studier states that $PER% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within $E of the true proportion. How large a sample is necessary?</div>@
qu.4.2.answer=1@
qu.4.2.choice.1=$Ans@
qu.4.2.choice.2=$Alt1@
qu.4.2.choice.3=$Alt2@
qu.4.2.choice.4=$Alt3@
qu.4.2.fixed=@

qu.4.3.mode=Multiple Choice@
qu.4.3.name=15b. Cardiac Pacemakers@
qu.4.3.comment=<p>The confidence interval would be:<br />
<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><msub><mi>Z</mi><mrow><mi mathvariant='normal'>$CL</mi></mrow></msub><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow></mstyle></math><br />
= <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><mi mathvariant='normal'>$Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac></mrow></msqrt></mrow></mrow></mstyle></math><br />
=&nbsp; <font size="3" face="Times New Roman">($Ans1, $Ans2)</font></p>@
qu.4.3.editing=useHTML@
qu.4.3.solution=@
qu.4.3.algorithm=$Q="15b";
$Pick=rint(4);
$Device=switch($Pick,"cardiac pacemaker","automated insulin pump","remote blood glucose monitor","medical telemetry unit");
$AorAn=switch($Pick,"a","an","a","a");
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$N=range(500,600);
$P=range(0.1,0.5,0.01);
$SE=sqrt($P*(1-$P)/($N));
$Ans1=decimal(4,$P-$Z*$SE);
$Ans2=decimal(4,$P+$Z*$SE);
$Alt11=decimal(4,range(1.1,1.9,0.01)*$Ans1);
$Alt12=decimal(4,range(1.1,1.9,0.01)*$Ans2);
condition:gt($Alt12,$Alt11);
$Alt21=decimal(4,range(0.5,0.9,0.01)*$Ans1);
$Alt22=decimal(4,range(0.5,0.9,0.01)*$Ans2);
condition:gt($Alt22,$Alt21);
$Alt31=decimal(4,0.5*($Ans1+switch(rint(2),$Alt11,$Alt21)));
$Alt32=decimal(4,0.5*($Ans2+switch(rint(2),$Alt12,$Alt22)));
condition:gt($Alt32,$Alt31);
$PER=$P*100;@
qu.4.3.uid=25ad3014-1e8a-4ecd-834d-3130f9340228@
qu.4.3.info=  Course=202;
  Type=MC;
@
qu.4.3.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>Researchers tested patients fitted with $AorAn $Device to see if use of a cellular telephone interferes with the operation of the device. There were $N tests conducted for one type of cellular telephone; interference with the device was found in $PER% of these tests.
<p>Which of the following is a&nbsp; $CL% Confidence Interval?&nbsp; Hint: use the General confidence interval for p.</p>
</div>@
qu.4.3.answer=1@
qu.4.3.choice.1=($Ans1, $Ans2)@
qu.4.3.choice.2=($Alt11, $Alt12)@
qu.4.3.choice.3=($Alt21, $Alt22)@
qu.4.3.choice.4=($Alt31, $Alt32)@
qu.4.3.fixed=@

qu.4.4.mode=Multiple Choice@
qu.4.4.name=11. Home gardens/decks/etc.@
qu.4.4.comment=<p>For a $CL% confidence level we have <font size="2" face="Times New Roman"><em>Z</em> = $Z</font>. Use the fact that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>by substituting in the known values and solving for <em><font size="3" face="Times New Roman">n</font> </em>:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Z</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math> , <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$Z</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>$P</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><msup><mi mathvariant='normal'>$E</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&simeq;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math></p>@
qu.4.4.editing=useHTML@
qu.4.4.solution=@
qu.4.4.algorithm=$Q="11";
$WhatPick=rint(4);
$What=switch($WhatPick,"vegetable gardens","flower garden","deck","gazebo");
$Align=switch(rint(2),"Left","Right");
$Which=switch($WhatPick,"Vegetable","Flower","Deck","Gazebo");
$N=range(600,700,10);
$n=range(100,200,10);
$P=range(0.1,0.9,0.01);
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$E=range(0.01,0.05,0.01);
$Ans=decimal(0,($Z^2)*$P*(1-$P)/($E^2));
$Alt1=int(range(1.1,1.9,0.01)*$Ans);
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));
$PER=decimal(1,$P*100);@
qu.4.4.uid=a6eccaba-7ac1-4f82-8a02-9421d8ce3b3c@
qu.4.4.info=  Course=202;
  Type=MC;
@
qu.4.4.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><img hspace="4" align="$Align" title="$What [IMG:$Which.gif]" alt="$What" src="__BASE_URI__CI/NormalProportion/$Which.gif" />A report states that $PER% of home owners had a $What. How large a sample is needed to estimate the true proportion of home owners who have $What\\s to within&nbsp;$E with $CL% confidence?<a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a></div>@
qu.4.4.answer=1@
qu.4.4.choice.1=$Ans@
qu.4.4.choice.2=$Alt1@
qu.4.4.choice.3=$Alt2@
qu.4.4.choice.4=$Alt3@
qu.4.4.fixed=@

qu.4.5.mode=Multiple Choice@
qu.4.5.name=03. Mice@
qu.4.5.comment=@
qu.4.5.editing=useHTML@
qu.4.5.solution=@
qu.4.5.algorithm=$Q="03";
$Z=1.96;
$P=range(0.5,0.9,0.01);
$N=range(500,600,1);
$SE=sqrt($P*(1-$P)/($N));
$ANS1=decimal(3,$P-$Z*$SE);
$ANS2=decimal(3,$P+$Z*$SE);
$ALT21=range(0.1,0.2,0.001);
$ALT22=range(0.2,0.4,0.001);
$ALT31=range(0.1,0.2,0.001);
$ALT32=range(0.2,0.3,0.001);
$PER=$P*100;
$ALT11=range(0.1,0.2,0.001);
$ALT12=range(0.2,0.3,0.001);@
qu.4.5.uid=2cf0b2c2-ea93-43e4-bdbd-ca2c9215ea6a@
qu.4.5.info=  Type=MC;
  Course=202;
@
qu.4.5.question=<div title="STAT202/Confidence Intervals/Confidence Intervals/Q$Q [1-$Q]"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/calculator.gif" /></a>In a sample of $N&nbsp;mice, a biologist found that $PER% were able to run a maze in 30 seconds or less. Find the 95% limit for the population proportion of mice who can run that maze in 30 seconds or less.</div>@
qu.4.5.answer=3@
qu.4.5.choice.1=$ALT11% < p < $ALT12%@
qu.4.5.choice.2=$ALT21% < p < $ALT22%@
qu.4.5.choice.3=$ANS1% < p < $ANS2%@
qu.4.5.choice.4=$ALT31% < p < $ALT32%@
qu.4.5.fixed=@

qu.4.6.mode=Multiple Choice@
qu.4.6.name=21A. Garden II@
qu.4.6.comment=@
qu.4.6.editing=useHTML@
qu.4.6.solution=@
qu.4.6.algorithm=$Q="21A";
$N=range(600,700,10);
$n=range(100,200,10);
$P=range(0.1,0.9,0.01);
$Z=2.326347874;
$E=range(0.01,0.05,0.01);
$ANS=decimal(0,($Z^2)*$P*(1-$P)/($E^2));
$ALT1=range(50,500,10);
$ALT2=range(50,500,10);
$ALT3=range(50,500,10);
$PER=decimal(1,$P*100);@
qu.4.6.uid=b37652d2-ca2a-41ae-bb9f-95d84cab7a30@
qu.4.6.question=<div title="STAT202/Test 7/Confidence Intervals/Q$Q [1-$Q]">A report states that $PER% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within&nbsp;$E with 98% confidence?</div>@
qu.4.6.answer=4@
qu.4.6.choice.1=$ALT3@
qu.4.6.choice.2=$ALT2@
qu.4.6.choice.3=$ALT1@
qu.4.6.choice.4=$ANS@
qu.4.6.fixed=@

qu.4.7.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a>A $School believes that $PER% of applicants to that school have parents who $DidWhat. How large a sample is needed to estimate the true proportion of students who have parents who $DidWhat to within&nbsp;$E with 95% confidence? (4 decimal accuracy)</div>@
qu.4.7.answer.num=$Ans@
qu.4.7.answer.units=@
qu.4.7.showUnits=false@
qu.4.7.grading=toler_abs@
qu.4.7.err=1@
qu.4.7.negStyle=minus@
qu.4.7.numStyle=thousands scientific dollars arithmetic@
qu.4.7.mode=Numeric@
qu.4.7.name=12a. Student's parents status@
qu.4.7.comment=<p>Use the fact that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>. For a 95% confidence level Z = $Z, so in this case:<br />
<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Z</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math> , solving:&nbsp; <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msup><mi mathvariant='normal'>$Z</mi><mrow><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>$P</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><msup><mi mathvariant='normal'>$E</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&simeq;</mo><mi mathvariant='normal'>$Ans</mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math></p>
<p>You need to round off to the integer since you cannot take a fraction of a student.</p>@
qu.4.7.editing=useHTML@
qu.4.7.solution=@
qu.4.7.algorithm=$Q="12a";
$School=switch(rint(3),"college","trade school","cooking school");
$DidWhat=switch(rint(3),"have remarried","were alumni","cannot help the student financially");
$N=range(600,700,10);
$n=range(100,200,10);
$P=range(0.1,0.9,0.01);
$Z=1.959963985;
$E=range(0.01,0.05,0.01);
$Ans=int(0.5+$Z^2*$P*(1-$P)/$E^2);
$PER=decimal(1,$P*100);@
qu.4.7.uid=04a4ed5d-e463-4894-bc26-44fbf00c29ad@
qu.4.7.info=  Type=numeric;
  Course=202;
@

qu.4.8.mode=Multiple Choice@
qu.4.8.name=06. Bartenders & gripes@
qu.4.8.comment=@
qu.4.8.editing=useHTML@
qu.4.8.solution=@
qu.4.8.algorithm=@
qu.4.8.uid=c20eea6f-dbbd-41e6-ad80-891bca91a16d@
qu.4.8.info=  Course=202;
  Algorithmic=no;
@
qu.4.8.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q06"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>In a sample of 855 bartenders, 48% heard complaints from patrons about work. If the margin of error was 4.4%, what was the confidence level that was used?</div>@
qu.4.8.answer=4@
qu.4.8.choice.1=90%@
qu.4.8.choice.2=95%@
qu.4.8.choice.3=98%@
qu.4.8.choice.4=99%@
qu.4.8.fixed=@

qu.4.9.mode=Inline@
qu.4.9.name=01. Racing car $@
qu.4.9.comment=@
qu.4.9.editing=useHTML@
qu.4.9.solution=@
qu.4.9.algorithm=$Q=1;
$Which=rint(5);
$Align=switch(rint(2),"Left","Right");@
qu.4.9.uid=e2054883-3528-41b8-af51-0ccb1f3eb522@
qu.4.9.info=  Type=numericx2;
  Course=202;
  Algorithmic=no;
@
qu.4.9.weighting=1,1@
qu.4.9.numbering=alpha@
qu.4.9.part.1.name=sro_id_1@
qu.4.9.part.1.answer.units=@
qu.4.9.part.1.numStyle=thousands scientific  arithmetic@
qu.4.9.part.1.editing=useHTML@
qu.4.9.part.1.showUnits=false@
qu.4.9.part.1.err=0.01@
qu.4.9.part.1.question=(Unset)@
qu.4.9.part.1.mode=Numeric@
qu.4.9.part.1.grading=toler_abs@
qu.4.9.part.1.negStyle=minus@
qu.4.9.part.1.answer.num=0.148@
qu.4.9.part.2.name=sro_id_2@
qu.4.9.part.2.answer.units=@
qu.4.9.part.2.numStyle=thousands scientific  arithmetic@
qu.4.9.part.2.editing=useHTML@
qu.4.9.part.2.showUnits=false@
qu.4.9.part.2.err=0.01@
qu.4.9.part.2.question=(Unset)@
qu.4.9.part.2.mode=Numeric@
qu.4.9.part.2.grading=toler_abs@
qu.4.9.part.2.negStyle=minus@
qu.4.9.part.2.answer.num=0.252@
qu.4.9.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><img hspace="4" align="$Align" src="__BASE_URI__CI/NormalProportion/Car$Which.gif" alt="Car" title="Car [IMG:Car$Which.gif]" />A sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% confidence interval of the true proportion of cars costing over $700,000 (3 decimals)? <br /><p>&nbsp;</p><p><span>&nbsp;</span><1><span>&nbsp; </span>< p < <span>&nbsp;</span><2><span>&nbsp;</span><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img hspace="4" border="0" align="absMiddle" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a></p></div>@

qu.4.10.mode=Multiple Choice@
qu.4.10.name=17. Risky companies@
qu.4.10.comment=<p>Since <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow></mstyle></math>, <font size="3" face="Times New Roman"><em>SE</em></font> is maximized by setting <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></mstyle></math>. Do so and solve for <font size="3" face="Times New Roman"><em>n</em></font>:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><msup><mi mathvariant='normal'>$SE</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math></p>@
qu.4.10.editing=useHTML@
qu.4.10.solution=@
qu.4.10.algorithm=$Q="17";
$SE=range(0.01,0.02,0.001);
$P=0.5;
$Ans=int($P*(1-$P)/$SE^2);
$Alt1=int(range(1.1,1.9,0.01)*$Ans);
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));
$PER=$P*100;@
qu.4.10.uid=9e089324-90f9-4db6-b148-147567e1f134@
qu.4.10.info=  Course=202;
  Type=MC;
@
qu.4.10.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q">Suppose a study is being planned to estimate the relative frequency of companies that are labeled as risky. What sample size is needed so that the standard error will be no larger than $SE.
<p>Hint: Find p that maximizes the standard error.</p>
</div>@
qu.4.10.answer=1@
qu.4.10.choice.1=$Ans@
qu.4.10.choice.2=$Alt1@
qu.4.10.choice.3=$Alt2@
qu.4.10.choice.4=$Alt3@
qu.4.10.fixed=@

qu.4.11.mode=Multiple Choice@
qu.4.11.name=21b. Voters@
qu.4.11.comment=<p>To find a $CL% confidence interval not that we have Z = $Z, p = $P and:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow></mrow><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>Z</mi></mrow><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math></p>
<p><font size="3" face="Times New Roman">$Ans1 < <em>p</em> < $Ans2</font></p>@
qu.4.11.editing=useHTML@
qu.4.11.solution=@
qu.4.11.algorithm=$Q="21b";
$Who=switch(rint(4),"voters","men","women","seniors");
$Which=rint(6);
$AP=rint(2);
$Align=switch($AP,"Left","Right");
$CAlign=switch($AP,"Right","Left");
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$N=range(500,600,1);
$P=range(0.1,0.5,0.01);
$SE=sqrt($P*(1-$P)/($N));
$Ans1=decimal(4,$P-$Z*$SE);
$Ans2=decimal(4,$P+$Z*$SE);
$Alt11=decimal(4,range(1.1,1.9,0.01)*$Ans1);
$Alt12=decimal(4,range(1.1,1.9,0.01)*$Ans2);
condition:lt($Alt11,$Alt12);
$Alt21=decimal(4,range(0.5,0.9,0.01)*$Ans1);
$Alt22=decimal(4,range(0.5,0.9,0.01)*$Ans2);
condition:lt($Alt21,$Alt22);
$Alt31=decimal(4,0.5*($Ans1+switch(rint(2),$Alt11,$Alt21)));
$Alt32=decimal(4,0.5*($Ans2+switch(rint(2),$Alt12,$Alt22)));
condition:lt($Alt31,$Alt32);
$PER=$P*100;@
qu.4.11.uid=01b67eab-5c0a-4d99-bc65-808b97220faf@
qu.4.11.info=  Course=202;
  Type=MC;
@
qu.4.11.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img hspace="4" border="0" align="$CAlign" src="__BASE_URI__Tools/Calculator.gif" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" /></a><img hspace="4" align="$Align" title="Voting [IMG:Vote$Which.gif]" alt="Voting" src="__BASE_URI__CI/NormalProportion/Vote$Which.gif" />A random sample of $N $Who found that $PER% were going to vote for a certain candidate. Find the $CL% limit for the population proportion of $Who who will vote for that candidate.</div>@
qu.4.11.answer=1@
qu.4.11.choice.1=$Ans1 < <font size="3" face="Times New Roman"><em>p</em></font> < $Ans2@
qu.4.11.choice.2=$Alt11 < <font size="3" face="Times New Roman"><em>p</em></font> < $Alt12@
qu.4.11.choice.3=$Alt21 < <font size="3" face="Times New Roman"><em>p</em></font> < $Alt22@
qu.4.11.choice.4=$Alt31 < <font size="3" face="Times New Roman"><em>p</em></font> < $Alt32@
qu.4.11.fixed=@

qu.4.12.mode=Multiple Choice@
qu.4.12.name=07. Smokers@
qu.4.12.comment=@
qu.4.12.editing=useHTML@
qu.4.12.solution=@
qu.4.12.algorithm=$Q="07";
$N=range(1000,1500,10);
$n=range(100,200,10);
$P=$n/$N;
$Z=2.326347874;
$E=range(0.01,0.05,0.01);
$Ans=decimal(0,($Z^2)*$P*(1-$P)/($E^2));
condition:lt($Ans,$N-50);
$Alt1=$Ans+int(range(0.2,0.9,0.01)*($N-$Ans));
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));
$PER=decimal(1,$P*100);@
qu.4.12.uid=9189007d-66fa-401c-821f-87db407b0a9a@
qu.4.12.info=  Course=202;
  Type=MC;
@
qu.4.12.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>A recent poll of $N people who work indoors found that&nbsp;$n of them smoke. If the researchers want to be 98% confident of their results to within $E, how large a sample is necessary?</div>@
qu.4.12.answer=1@
qu.4.12.choice.1=$Ans@
qu.4.12.choice.2=$Alt1@
qu.4.12.choice.3=$Alt2@
qu.4.12.choice.4=$Alt3@
qu.4.12.fixed=@

qu.4.13.mode=Multiple Choice@
qu.4.13.name=04. Speeding@
qu.4.13.comment=@
qu.4.13.editing=useHTML@
qu.4.13.solution=@
qu.4.13.algorithm=$Q="04";
$DC=rint(4);
$DriverClass=switch($DC,"teenage boys","married men","single women","grandparents");
$P=switch($DC,range(0.3,0.9,0.05),range(0.05,0.45,0.05),range(0.05,0.35,0.05),range(0.05,0.15,0.05));
$N=range(300,400,10);
$Z=maple("stats[statevalf,icdf,normald](0.95)");
$SE=sqrt($P*(1-$P)/($N));
$ANS1=decimal(3,$P-$Z*$SE);
$ANS2=decimal(3,$P+$Z*$SE);
$ALT21=range(0.1,0.2,0.001);
$ALT22=range(0.2,0.4,0.001);
$ALT31=range(0.1,0.2,0.001);
$ALT32=range(0.2,0.3,0.001);
$PER=$P*100;
$ALT11=range(0.1,0.2,0.001);
$ALT12=range(0.2,0.3,0.001);
$Which=rint(4);
$Align=switch(rint(2),"Left","Right");@
qu.4.13.uid=f6882da7-0431-4342-b3ca-86eb7410a4b5@
qu.4.13.info=  Course=202;
  Type=MC;
@
qu.4.13.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><img hspace="4" align="$Align" src="__BASE_URI__CI/NormalProportion/Car$Which.gif" alt="Car" title="Car [IMG:Car$Which.gif]" />It was found that in a sample of $N $DriverClass, $PER% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of $DriverClass who have received speeding tickets?
<p><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a></p>
</div>@
qu.4.13.answer=1@
qu.4.13.choice.1=$ANS1 < p < $ANS2@
qu.4.13.choice.2=$ALT11 < p < $ALT12@
qu.4.13.choice.3=$ALT21 < p < $ALT22@
qu.4.13.choice.4=$ALT31 < p < $ALT32@
qu.4.13.fixed=@

qu.4.14.mode=True False@
qu.4.14.name=09. Shoppers@
qu.4.14.comment=@
qu.4.14.editing=useHTML@
qu.4.14.solution=@
qu.4.14.algorithm=$Q="09";
$X=switch(rint(4),"A retailer wants to estimate with 99% confidence the number of people who buy at  his store. A previous study showed that 24% of those interviewed had shopped at his store. He wishes to be accurate within 3% of the true proportion. The minimum sample size necessary would be 1,100.","A retailer wants to estimate with 98% confidence the number of people who buy at  his store. A previous study showed that 22% of those interviewed had shopped at his store. He wishes to be accurate within 5% of the true proportion. The minimum sample size necessary would be 1,200.","A retailer wants to estimate with 95% confidence the number of people who buy at  his store. A previous study showed that 10% of those interviewed had shopped at his store. He wishes to be accurate within 5% of the true proportion. The minimum sample size necessary would be 2,100.");@
qu.4.14.uid=8e61c0f2-753f-40ba-8a56-ccd5bfceed3d@
qu.4.14.info=  Course=202;
  Type=T/F;
@
qu.4.14.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a>$X</div>@
qu.4.14.answer=2@
qu.4.14.choice.1=True@
qu.4.14.choice.2=False@
qu.4.14.fixed=@

qu.4.15.mode=Multiple Choice@
qu.4.15.name=20. Impulsive shoppers@
qu.4.15.comment=<p>To find a $CL% confidence interval not that we have Z = $Z, p = $P and:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow></mrow><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>Z</mi></mrow><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math></p>
<p><font size="3" face="Times New Roman">$Ans1 < <em>p</em> < $Ans2</font></p>@
qu.4.15.editing=useHTML@
qu.4.15.solution=@
qu.4.15.algorithm=$Q="20";
$Which=rint(5);
$AP=rint(2);
$Align=switch($AP,"Left","Right");
$CAlign=switch($AP,"Right","Left");
$Who=switch(rint(4),"women","adolescent","men","depressed");
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$N=range(500,600,1);
$P=range(0.1,0.5,0.01);
$SE=sqrt($P*(1-$P)/($N));
$Ans1=decimal(4,$P-$Z*$SE);
$Ans2=decimal(4,$P+$Z*$SE);
$Alt11=decimal(4,range(1.1,1.9,0.01)*$Ans1);
$Alt12=decimal(4,range(1.1,1.9,0.01)*$Ans2);
condition:lt($Alt11,$Alt12);
$Alt21=decimal(4,range(0.5,0.9,0.01)*$Ans1);
$Alt22=decimal(4,range(0.5,0.9,0.01)*$Ans2);
condition:lt($Alt21,$Alt22);
$Alt31=decimal(4,0.5*($Ans1+switch(rint(2),$Alt11,$Alt21)));
$Alt32=decimal(4,0.5*($Ans2+switch(rint(2),$Alt12,$Alt22)));
condition:lt($Alt31,$Alt32);
$PER=$P*100;@
qu.4.15.uid=b304ba23-5146-419e-acd0-65dc85551fbe@
qu.4.15.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><img hspace="4" align="$Align" src="__BASE_URI__CI/NormalProportion/Shopping$Which.gif" alt="Shopping" title="Shopping [IMG:Shopping$Which.gif]" />A survey of $N $Who shoppers found that $PER% of them shop on impulse. What is the $CL% confidence interval for the true proportion of $Who shoppers who shop on impulse?<a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="$CAlign" hspace="4" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a></div>@
qu.4.15.answer=1@
qu.4.15.choice.1=$Ans1 < <font size="3" face="Times New Roman"><em>p</em></font> < $Ans2@
qu.4.15.choice.2=$Alt11 < <font size="3" face="Times New Roman"><em>p</em></font> < $Alt12@
qu.4.15.choice.3=$Alt21 < <font size="3" face="Times New Roman"><em>p</em></font> < $Alt22@
qu.4.15.choice.4=$Alt31 < <font size="3" face="Times New Roman"><em>p</em></font> < $Alt32@
qu.4.15.fixed=@

qu.4.16.mode=Multiple Choice@
qu.4.16.name=32A: Number of n@
qu.4.16.comment=@
qu.4.16.editing=useHTML@
qu.4.16.solution=@
qu.4.16.algorithm=$Q="32A";
$SE=range(0.01,0.02,0.001);
$P=range(0.5,0.99,0.01);
$ANS=decimal(0,($P*(1-$P)/$SE^2)-4);
$ALT1=$ANS+range(10,20,1);
$ALT2=$ANS+range(20,30,1);
$ALT3=$ANS+range(30,40,1);
$PER=$P*100;@
qu.4.16.uid=d5ea33b4-7e55-4602-b64c-32e726584cdb@
qu.4.16.question=<p>In a study of human mortality rate, an Actuary estimated that in US and Canada, about $PER% (fictional figures) of life insurance claims resulted from accidental deaths. Suppose a study is being planned to estimate the relative frequency of claims in Canada, and it is desired that the standard error of the esrimated relative frequency should be $SE. How many claims should be included in the study.</p>@
qu.4.16.answer=1@
qu.4.16.choice.1=$ANS@
qu.4.16.choice.2=$ALT1@
qu.4.16.choice.3=$ALT2@
qu.4.16.choice.4=$ALT3@
qu.4.16.fixed=@

qu.4.17.mode=Multiple Choice@
qu.4.17.name=02. Printers@
qu.4.17.comment=@
qu.4.17.editing=useHTML@
qu.4.17.solution=@
qu.4.17.algorithm=$Q="02";
$n=range(50,80);
$Z=2.575829304;
$N=range(500,600);
$P=$n/$N;
$SE=sqrt($P*(1-$P)/($N));
$ANS1=decimal(3,$P-$Z*$SE);
$ANS2=decimal(3,$P+$Z*$SE);
$ALT21=range(0.1,0.2,0.001);
$ALT22=range(0.2,0.4,0.001);
$ALT31=range(0.1,0.2,0.001);
$ALT32=range(0.2,0.3,0.001);
$PER=$P*100;
$ALT11=range(0.1,0.2,0.001);
$ALT12=range(0.2,0.3,0.001);@
qu.4.17.uid=b6a81c25-1941-462d-8271-138899862e03@
qu.4.17.info=  Type=MC;
  Course=202;
@
qu.4.17.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>A random sample of&nbsp;$N printers discovered that&nbsp;$n of them were being used in small businesses . Find the 99% limit for the population proportion of printers that are used in small businesses.</div>@
qu.4.17.answer=2@
qu.4.17.choice.1=$ALT11 < p < $ALT12@
qu.4.17.choice.2=$ANS1 < p < $ANS2@
qu.4.17.choice.3=$ALT21 < p < $ALT22@
qu.4.17.choice.4=$ALT31 < p < $ALT32@
qu.4.17.fixed=@

qu.4.18.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:calculator.gif]" /></a>In a study of human mortality rate, an Actuary estimated that in US and Canada, about $PER% (fictional figures) of life insurance claims resulted from accidental deaths. Suppose a study is being planned to estimate the relative frequency of claims in Canada, and it is desired that the standard error of the estimated relative frequency should be $SE. How many claims should be included in the study?</div>@
qu.4.18.answer.num=$Ans@
qu.4.18.answer.units=@
qu.4.18.showUnits=false@
qu.4.18.grading=exact_value@
qu.4.18.negStyle=minus@
qu.4.18.numStyle=thousands scientific dollars arithmetic@
qu.4.18.mode=Numeric@
qu.4.18.name=16. Human Mortality@
qu.4.18.comment=<p>Since <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow></mstyle></math>we can solve for n to get:&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><msup><mi>SE</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><msup><mi mathvariant='normal'>$SE</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math></p>@
qu.4.18.editing=useHTML@
qu.4.18.solution=@
qu.4.18.algorithm=$Q=16;
$SE=range(0.01,0.02,0.001);
$P=range(0.5,0.99,0.01);
$Ans=int($P*(1-$P)/$SE^2);

$PER=$P*100;@
qu.4.18.uid=75d159b5-416c-43cc-9d90-95f59b107c17@
qu.4.18.info=  Course=202;
  Type=numeric;
@

qu.4.19.mode=Inline@
qu.4.19.name=21a. Voters@
qu.4.19.comment=<p>To find a $CL% confidence interval not that we have Z = $Z, p = $P and:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow></mrow><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>Z</mi></mrow><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math></p>
<p><font size="3" face="Times New Roman">$Ans1 < <em>p</em> < $Ans2</font></p>@
qu.4.19.editing=useHTML@
qu.4.19.solution=@
qu.4.19.algorithm=$Q="21a";
$Who=switch(rint(4),"voters","men","women","seniors");
$Which=rint(6);
$AP=rint(2);
$Align=switch($AP,"Left","Right");
$CAlign=switch($AP,"Right","Left");
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$N=range(500,600,1);
$P=range(0.1,0.5,0.01);
$SE=sqrt($P*(1-$P)/($N));
$Ans1=decimal(4,$P-$Z*$SE);
$Ans2=decimal(4,$P+$Z*$SE);
$Alt11=decimal(4,range(1.1,1.9,0.01)*$Ans1);
$Alt12=decimal(4,range(1.1,1.9,0.01)*$Ans2);
condition:lt($Alt11,$Alt12);
$Alt21=decimal(4,range(0.5,0.9,0.01)*$Ans1);
$Alt22=decimal(4,range(0.5,0.9,0.01)*$Ans2);
condition:lt($Alt21,$Alt22);
$Alt31=decimal(4,0.5*($Ans1+switch(rint(2),$Alt11,$Alt21)));
$Alt32=decimal(4,0.5*($Ans2+switch(rint(2),$Alt12,$Alt22)));
condition:lt($Alt31,$Alt32);
$PER=$P*100;@
qu.4.19.uid=610882b1-11a2-40a4-846c-200e7101450b@
qu.4.19.info=  Course=202;
  Type=numericx2;
@
qu.4.19.weighting=1,1@
qu.4.19.numbering=alpha@
qu.4.19.part.1.name=sro_id_1@
qu.4.19.part.1.answer.units=@
qu.4.19.part.1.numStyle=thousands scientific  arithmetic@
qu.4.19.part.1.editing=useHTML@
qu.4.19.part.1.showUnits=false@
qu.4.19.part.1.question=(Unset)@
qu.4.19.part.1.mode=Numeric@
qu.4.19.part.1.grading=exact_value@
qu.4.19.part.1.negStyle=minus@
qu.4.19.part.1.answer.num=$Ans1@
qu.4.19.part.2.name=sro_id_2@
qu.4.19.part.2.answer.units=@
qu.4.19.part.2.numStyle=thousands scientific  arithmetic@
qu.4.19.part.2.editing=useHTML@
qu.4.19.part.2.showUnits=false@
qu.4.19.part.2.question=(Unset)@
qu.4.19.part.2.mode=Numeric@
qu.4.19.part.2.grading=exact_value@
qu.4.19.part.2.negStyle=minus@
qu.4.19.part.2.answer.num=$Ans2@
qu.4.19.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img hspace="4" border="0" align="$CAlign" src="__BASE_URI__Tools/Calculator.gif" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" /></a><img hspace="4" align="$Align" title="Voting [IMG:Vote$Which.gif]" alt="Voting" src="__BASE_URI__CI/NormalProportion/Vote$Which.gif" />A random sample of $N $Who found that $PER% were going to vote for a certain candidate. Find the $CL% limit for the population proportion of $Who who will vote for that candidate.<span>&nbsp;</span><p><1><span>&nbsp; <font size="3" face="Times New Roman">< <em>p</em>&nbsp; <</font>&nbsp;<span>&nbsp;</span><2><span>&nbsp;</span> </span></p></div>@

qu.4.20.mode=Multiple Choice@
qu.4.20.name=05. Pizza@
qu.4.20.comment=@
qu.4.20.editing=useHTML@
qu.4.20.solution=@
qu.4.20.algorithm=$Q="05";
$PType=switch(rint(4),"cheese","pepperoni","a deluxe speciality","vegetarian");
$n=range(20,40,1);
$Z=maple("stats[statevalf,icdf,normald](0.995)");
$N=range(100,150,1);
$P=$n/$N;
$SE=sqrt($P*(1-$P)/($N));
$ANS1=decimal(3,$P-$Z*$SE);
$ANS2=decimal(3,$P+$Z*$SE);
$ALT21=range(0.1,0.2,0.001);
$ALT22=range(0.2,0.4,0.001);
$ALT31=range(0.1,0.2,0.001);
$ALT32=range(0.2,0.3,0.001);
$PER=$P*100;
$ALT11=range(0.1,0.2,0.001);
$ALT12=range(0.2,0.3,0.001);
$Which=rint(4);
$Align=switch(rint(2),"Left","Right");@
qu.4.20.uid=7e5f291a-b1cd-4799-ab21-ce14e7c5c026@
qu.4.20.info=  Course=202;
  Type=MC;
@
qu.4.20.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><img hspace="4" align="$Align" src="__BASE_URI__CI/NormalProportion/Pizza$Which.gif" alt="Pizza" title="Pizza [IMG:Pizza$Which.gif]" />The Pizza Shop wanted to determine what proportion of its customers ordered only $PType pizza. Out of&nbsp;$N customers surveyed,&nbsp;$n ordered $PType pizza. What is the 99% confidence interval of the true proportion of customers who order only $PType pizza?<a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a></div>@
qu.4.20.answer=1@
qu.4.20.choice.1=$ANS1 < p < $ANS2@
qu.4.20.choice.2=$ALT11 < p < $ALT12@
qu.4.20.choice.3=$ALT21 < p < $ALT22@
qu.4.20.choice.4=$ALT31 < p < $ALT32@
qu.4.20.fixed=@

qu.4.21.mode=Multiple Choice@
qu.4.21.name=03. Mice@
qu.4.21.comment=@
qu.4.21.editing=useHTML@
qu.4.21.solution=@
qu.4.21.algorithm=$Q=3;
$Z=1.96;
$P=range(0.5,0.9,0.01);
$N=range(500,700,10);
$Y=decimal(0,$N*$P);
$PW=($Y+0.5*$Z^2)/($N+$Z^2);
$SE=sqrt($P*(1-$P)/($N+$Z^2));
$ANS1=decimal(3,$PW-$Z*$SE);
$ANS2=decimal(3,$PW+$Z*$SE);
$ALT21=range(0.1,0.2,0.001);
$ALT22=range(0.2,0.4,0.001);
$ALT31=range(0.1,0.2,0.001);
$ALT32=range(0.2,0.3,0.001);
$PER=$P*100;
$ALT11=range(0.1,0.2,0.001);
$ALT12=range(0.2,0.3,0.001);@
qu.4.21.uid=8ec54e54-8df4-4b8f-ad5e-c98e72165885@
qu.4.21.info=  Course=202;
  Type=MC;
@
qu.4.21.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>In a sample of $N mice, a biologist found that $PER% were able to run a maze in 30 seconds or less. Find the 95% limit for the population proportion of mice who can run that maze in 30 seconds or less.</div>@
qu.4.21.answer=3@
qu.4.21.choice.1=$ALT11% < p < $ALT12%@
qu.4.21.choice.2=$ALT21% < p < $ALT22%@
qu.4.21.choice.3=$ANS1% < p < $ANS2%@
qu.4.21.choice.4=$ALT31% < p < $ALT32%@
qu.4.21.fixed=@

qu.4.22.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>A&nbsp; manager of a $Store estimated that $PER% of customers use coupons in their purchases. How large a sample is required to estimate the true proportion to within&nbsp;$E with $CL% confidence?</div>@
qu.4.22.answer.num=$Ans@
qu.4.22.answer.units=@
qu.4.22.showUnits=false@
qu.4.22.grading=exact_value@
qu.4.22.negStyle=minus@
qu.4.22.numStyle=thousands scientific dollars arithmetic@
qu.4.22.mode=Numeric@
qu.4.22.name=14. Discount coupons@
qu.4.22.comment=<p>For a $CL% confidence level we have Z = $Z. Use the fact that&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math> by substituting in the known values and solving for n :</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Z</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$Z</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>$P</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><msup><mi mathvariant='normal'>$E</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&simeq;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math></p>@
qu.4.22.editing=useHTML@
qu.4.22.solution=@
qu.4.22.algorithm=$Q="14";
$Store=switch(rint(3),"supermarket","department store","discount warehouse");
$N=range(600,700,10);
$n=range(100,200,10);
$P=range(0.1,0.9,0.01);
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$E=range(0.01,0.05,0.01);
$Ans=int($Z^2*$P*(1-$P)/$E^2);
$PER=decimal(1,$P*100);@
qu.4.22.uid=e1df1276-1424-4f64-a918-73c1425dd65f@
qu.4.22.info=  Type=numeric;
  Course=202;
@

qu.4.23.mode=Multiple Choice@
qu.4.23.name=19. Groups & Internet Usage@
qu.4.23.comment=<p>For a <font size="3" face="Times New Roman">$CL</font>% confidence interval we have <font size="3" face="Times New Roman"><em>Z</em> = $Z</font>&nbsp; and <font size="3" face="Times New Roman"><em>p</em> = $P</font> so the interval is:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi></mi></mrow><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>Z</mi></mrow><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$n</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo></mrow></mstyle></math>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$n</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math></p>
<p><font size="3" face="Times New Roman">$Ans1 <<em> p</em> < $Ans2</font></p>@
qu.4.23.editing=useHTML@
qu.4.23.solution=@
qu.4.23.algorithm=$Q="19";
$Group=switch(rint(4),"women","seniors","unsupervised children","employees at work");
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$N=range(500,600);
$P=range(0.1,0.5,0.01);
$SE=sqrt($P*(1-$P)/($N));
$Ans1=decimal(4,$P-$Z*$SE);
$Ans2=decimal(4,$P+$Z*$SE);
$Alt11=decimal(4,range(1.1,1.9,0.01)*$Ans1);
$Alt12=decimal(4,range(1.1,1.9,0.01)*$Ans2);
condition:lt($Alt11,$Alt12);
$Alt21=decimal(4,range(0.5,0.9,0.01)*$Ans1);
$Alt22=decimal(4,range(0.5,0.9,0.01)*$Ans2);
condition:lt($Alt21,$Alt22);
$Alt31=decimal(4,0.5*($Ans1+switch(rint(2),$Alt11,$Alt21)));
$Alt32=decimal(4,0.5*($Ans2+switch(rint(2),$Alt12,$Alt22)));
condition:lt($Alt31,$Alt32);
$PER=$P*100;@
qu.4.23.uid=2e7f1ef3-aa0b-4f4e-b6c3-a11b578427e0@
qu.4.23.info=  Course=202;
  Type=MC;
@
qu.4.23.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>A recent study of $N Internet users in Europe found that $PER% of Internet users were $Group. What is the $CL% confidence interval of the true proportion of $Group in Europe who use the Internet?</div>@
qu.4.23.answer=1@
qu.4.23.choice.1=$Ans1< p < $Ans2@
qu.4.23.choice.2=$Alt11 < p < $Alt12@
qu.4.23.choice.3=$Alt21 < p < $Alt22@
qu.4.23.choice.4=$Alt31 < p < $Alt32@
qu.4.23.fixed=@

qu.4.24.mode=Multiple Choice@
qu.4.24.name=13. Find error@
qu.4.24.comment=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>Z</mi><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac></mrow></msqrt><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math> where we have used the fact that for a $CL% confidence interval, <font size="3" face="Times New Roman"><em>Z</em> = $Z</font> .</p>@
qu.4.24.editing=useHTML@
qu.4.24.solution=@
qu.4.24.algorithm=$Q="13";
$P=range(0.1,0.9,0.01);
$N=range(1000,1500,10);
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$Ans = decimal(4,$Z*SQRT(($P)*(1-$P)/$N));
$Alt1=decimal(4,range(1.1,1.9,0.01)*$Ans);
$Alt2=decimal(4,range(0.5,0.9,0.01)*$Ans);
$Alt3=decimal(4,0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));@
qu.4.24.uid=e1125582-a5fa-41c0-aa6d-8f122237da8b@
qu.4.24.info=  Type=MC;
  Course=202;
@
qu.4.24.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a>A sample of&nbsp;$N was used to estimate a proportion with $CL% confidence. If p = $P, what was the amount of error?</div>@
qu.4.24.answer=1@
qu.4.24.choice.1=$Ans@
qu.4.24.choice.2=$Alt1@
qu.4.24.choice.3=$Alt2@
qu.4.24.choice.4=$Alt3@
qu.4.24.fixed=@

qu.4.25.mode=Multiple Choice@
qu.4.25.name=12b. Student's parents status@
qu.4.25.comment=<p>Use the fact that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>. For a 95% confidence level Z = $Z, so in this case:<br />
<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$E</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Z</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math> , solving:&nbsp; <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$Z</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>$P</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><msup><mi mathvariant='normal'>$E</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&simeq;</mo><mi mathvariant='normal'>$Ans</mi></mrow></mstyle></math></p>@
qu.4.25.editing=useHTML@
qu.4.25.solution=@
qu.4.25.algorithm=$Q="12b";
$School=switch(rint(3),"college","trade school","cooking school");
$DidWhat=switch(rint(3),"have remarried","were alumni","cannot help the student financially");
$N=range(600,700,10);
$n=range(100,200,10);
$P=range(0.1,0.9,0.01);
$Z=1.959963985;
$E=range(0.01,0.05,0.01);
$Ans=int($Z^2*$P*(1-$P)/$E^2);
$Alt1=int(range(1.1,1.9,0.01)*$Ans);
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));
$PER=decimal(1,$P*100);@
qu.4.25.uid=f7d130c4-e7c8-4a11-847c-99b1a1bda8a8@
qu.4.25.info=  Type=MC;
  Course=202;
@
qu.4.25.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>A $School believes that $PER% of applicants to that school have parents who $DidWhat. How large a sample is needed to estimate the true proportion of students who have parents who $DidWhat to within&nbsp;$E with 95% confidence?</div>@
qu.4.25.answer=1@
qu.4.25.choice.1=$Ans@
qu.4.25.choice.2=$Alt1@
qu.4.25.choice.3=$Alt2@
qu.4.25.choice.4=$Alt3@
qu.4.25.fixed=@

qu.4.26.mode=Multiple Choice@
qu.4.26.name=18. Stock Options@
qu.4.26.comment=<p>First <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>p</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mi mathvariant='normal'>$n</mi><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$P</mi></mrow></mstyle></math> . Then for a <font size="3" face="Times New Roman">$CL%</font> confidence interval we have <font size="3" face="Times New Roman"><em>Z</em> = $Z</font> so the interval is:</p>
<p>&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&pm;</mo><mi mathvariant='normal'>$Z</mi><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$n</mi></mrow></mfrac></mrow></msqrt><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$Ans1</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>$Ans2</mi></mrow></mfenced></mrow></mstyle></math></p>@
qu.4.26.editing=useHTML@
qu.4.26.solution=@
qu.4.26.algorithm=$Q=18;
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$n=range(50,60);
$N=range(100,200);
$P=decimal(3,$n/$N);
$SE=sqrt($P*(1-$P)/($N));
$Ans1=decimal(4,$P-$Z*$SE);
$Ans2=decimal(4,$P+$Z*$SE);
$Alt11=decimal(4,range(1.1,1.9,0.01)*$Ans1);
$Alt12=decimal(4,range(1.1,1.9,0.01)*$Ans2);
condition:lt($Alt11,$Alt12);
$Alt21=decimal(4,range(0.5,0.9,0.01)*$Ans1);
$Alt22=decimal(4,range(0.5,0.9,0.01)*$Ans2);
condition:lt($Alt21,$Alt22);
$Alt31=decimal(4,0.5*($Ans1+switch(rint(2),$Alt11,$Alt21)));
$Alt32=decimal(4,0.5*($Ans2+switch(rint(2),$Alt12,$Alt22)));
condition:lt($Alt31,$Alt32);
$PER=$P*100;@
qu.4.26.uid=b647e8a9-429e-4b9e-b4bc-637b53fd786d@
qu.4.26.info=  Course=202;
  Type=MC;
@
qu.4.26.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a target="Popup" href="__BASE_URI__Tools/NormalCalculator.htm" onclick="window.open(this.href,this.target,'height=140,width=340')"><img border="0" align="right" src="__BASE_URI__Tools/Calculator.gif" alt="Quick Normal/InvNormal Calculator" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" /></a>In a study of stock options, a sample of $N stock options were observed and $n were discovered to have a final negative payoff. Construct a $CL% confidence interval for the relative frequency of those stock options with negative payoff.</div>@
qu.4.26.answer=1@
qu.4.26.choice.1=($Ans1 , $Ans2)@
qu.4.26.choice.2=($Alt11, $Alt12)@
qu.4.26.choice.3=($Alt21, $Alt22)@
qu.4.26.choice.4=($Alt31, $Alt32)@
qu.4.26.fixed=@

qu.4.27.mode=Inline@
qu.4.27.name=15a. Cardiac Pacemakers@
qu.4.27.comment=<p>The confidence interval would be:<br />
<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><msub><mi>Z</mi><mrow><mi mathvariant='normal'>$CL</mi></mrow></msub><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mrow></mstyle></math><br />
= <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$P</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plusmn;</mo><mi mathvariant='normal'>$Z</mi><mrow><msqrt><mrow><mfrac><mrow><mi mathvariant='normal'>$P</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$P</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>$N</mi></mrow></mfrac></mrow></msqrt></mrow></mrow></mstyle></math><br />
=&nbsp; <font size="3" face="Times New Roman">($Ans1, $Ans2)</font></p>@
qu.4.27.editing=useHTML@
qu.4.27.solution=@
qu.4.27.algorithm=$Q="15a";
$Pick=rint(4);
$Device=switch($Pick,"cardiac pacemaker","automated insulin pump","remote blood glucose monitor","medical telemetry unit");
$AorAn=switch($Pick,"a","an","a","a");
$ZPick=rint(4);
$CL=switch($ZPick,90,95,98,99);
$Z=switch($ZPick,1.6449,1.9600,2.3263,2.5758);
$N=range(500,600);
$P=range(0.1,0.5,0.01);
$SE=sqrt($P*(1-$P)/($N));
$Ans1=decimal(4,$P-$Z*$SE);
$Ans2=decimal(4,$P+$Z*$SE);

$PER=$P*100;@
qu.4.27.uid=80249559-fa0b-4340-b952-5629e92ef7f0@
qu.4.27.info=  Course=202;
  Type=numericx2;
@
qu.4.27.weighting=1,1@
qu.4.27.numbering=alpha@
qu.4.27.part.1.name=sro_id_1@
qu.4.27.part.1.answer.units=@
qu.4.27.part.1.numStyle=thousands scientific  arithmetic@
qu.4.27.part.1.editing=useHTML@
qu.4.27.part.1.showUnits=false@
qu.4.27.part.1.err=0.0010@
qu.4.27.part.1.question=(Unset)@
qu.4.27.part.1.mode=Numeric@
qu.4.27.part.1.grading=toler_abs@
qu.4.27.part.1.negStyle=minus@
qu.4.27.part.1.answer.num=$Ans1@
qu.4.27.part.2.name=sro_id_2@
qu.4.27.part.2.answer.units=@
qu.4.27.part.2.numStyle=thousands scientific  arithmetic@
qu.4.27.part.2.editing=useHTML@
qu.4.27.part.2.showUnits=false@
qu.4.27.part.2.err=0.0010@
qu.4.27.part.2.question=(Unset)@
qu.4.27.part.2.mode=Numeric@
qu.4.27.part.2.grading=toler_abs@
qu.4.27.part.2.negStyle=minus@
qu.4.27.part.2.answer.num=$Ans2@
qu.4.27.question=<div title="UW Statistics Bank/Confidence Intervals/Normal (Proportion)/Q$Q"><a onclick="window.open(this.href,this.target,'height=140,width=340')" href="__BASE_URI__Tools/NormalCalculator.htm" target="Popup"><img border="0" align="right" title="Quick Normal/InvNormal Calculator [IMG:Calculator.gif]" alt="Quick Normal/InvNormal Calculator" src="__BASE_URI__Tools/Calculator.gif" /></a>Researchers tested patients fitted with $AorAn $Device to see if use of a cellular telephone interferes with the operation of the device. There were $N tests conducted for one type of cellular telephone; interference with the device was found in $PER% of these tests.<p>Construct a $CL% Conficence Interval&nbsp; (4 decimal accuracy).&nbsp; Hint: use the General confidence interval for p.&nbsp;</p><span>( </span><1><span>&nbsp; , <span>&nbsp;</span><2><span> </span>)<br /></span></div>@

qu.5.topic=Basics@

qu.5.1.mode=Multiple Choice@
qu.5.1.name=02. Risky companies@
qu.5.1.comment=<p>The standard error is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mfrac><mrow><mi>p</mi><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>p</mi></mrow></mfenced></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msqrt></mrow></mstyle></math>. This expression is maximized (for a given <em>n</em> ) when <em>p </em>= 0.5 . Substituting we want <em>n</em> such that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mfrac><mn>1</mn><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>n</mi></mrow></mfrac></mrow></msqrt><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mi mathvariant='normal'>$SE</mi></mrow></mstyle></math>,<br />
<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>n</mi></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><msup><mi mathvariant='normal'>$SE</mi><mrow><mn>2</mn></mrow></msup></mrow></mstyle></math>,<br />
<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>n</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&GreaterEqual;</mo><mrow><mfrac><mn>1</mn><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi mathvariant='normal'>$SE</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mrow></mstyle></math> which rounds to $Ans .</p>@
qu.5.1.editing=useHTML@
qu.5.1.solution=@
qu.5.1.algorithm=$Q="02";
$SE=range(0.01,0.02,0.001);
$P=0.5;
$Ans=decimal(0,($P*(1-$P)/$SE^2));
$Alt1=int(range(1.1,1.9,0.01)*$Ans);
$Alt2=int(range(0.5,0.9,0.01)*$Ans);
$Alt3=int(0.5*($Ans+switch(rint(2),$Alt1,$Alt2)));
$PER=$P*100;@
qu.5.1.uid=4c2acb6c-aee4-403f-ac0a-47da633e0590@
qu.5.1.info=  Course=202;
  Type=MC;
@
qu.5.1.question=<div title="UW Statistics Bank/Confidence Intervals/Basics/Q$Q">Suppose a study is being planned to estimate the relative frequency of companies that are labeled as risky. What sample size is needed so that the standard error will be no larger than $SE?
<p>Hint: Find p that maximizes the standard error.</p>
</div>@
qu.5.1.answer=1@
qu.5.1.choice.1=$Ans@
qu.5.1.choice.2=$Alt1@
qu.5.1.choice.3=$Alt2@
qu.5.1.choice.4=$Alt3@
qu.5.1.fixed=@

qu.5.2.mode=True False@
qu.5.2.name=04 . Interval estimate@
qu.5.2.comment=<p>Consider estimating a mean. While you know the sample mean, you do not know the actual mean - that is why you are constructing a confidence interval! At best you can be P% confidence that the mean lies in your interval, where P<100 - you can never be 100% certain. Thus the parameter may well be inside OR outside the interval.</p>@
qu.5.2.editing=useHTML@
qu.5.2.solution=@
qu.5.2.algorithm=@
qu.5.2.uid=d4b0d190-208f-4c6a-a0dd-6334e167476e@
qu.5.2.info=  Course=202;
  Type=T/F;
  Algorithmic=no;
@
qu.5.2.question=<div title="UW Statistics Bank/Confidence Intervals/Basics/Q4">An interval estimate may or may not contain the value of the parameter being estimated.</div>@
qu.5.2.answer=1@
qu.5.2.choice.1=True@
qu.5.2.choice.2=False@
qu.5.2.fixed=@

qu.5.3.mode=True False@
qu.5.3.name=05. SE vs SD@
qu.5.3.comment=<p>Since <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>SE</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><mfrac><mi>SD</mi><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mrow></mstyle></math>and the case where <font size="3" face="Times New Roman"><em>n</em></font> = 1 is trivial we always have SE < SD .</p>@
qu.5.3.editing=useHTML@
qu.5.3.solution=@
qu.5.3.algorithm=$Q=5;
$Pick=rint(3);
$X=switch($Pick,"larger than the standard deviation of the sample from which it was derived","equals the standard deviation of the sample from which it was derived","larger than the standard deviation of the population from which it was derived");@
qu.5.3.uid=685b3849-9c2e-499a-a626-b30921d92570@
qu.5.3.info=  Course=202;
  Type=T/F;
@
qu.5.3.question=<div title="UW Statistics Bank/Confidence Intervals/Basics/Q$Q">The (estimated) standard error of the mean is $X.</div>@
qu.5.3.answer=2@
qu.5.3.choice.1=True@
qu.5.3.choice.2=False@
qu.5.3.fixed=@

qu.5.4.mode=Multiple Choice@
qu.5.4.name=03. Identify a CI@
qu.5.4.comment=<img hspace="4" title="The $IntervalP% Confidence Interval [IMG:ConfidenceInterval$IntervalP.gif]" alt="" src="__BASE_URI__CI/Basics/ConfidenceInterval$IntervalP.gif" halign="Center" /><br />
The diagram shows us that the area outside the indicated points is 2($HalfTail) = $Tail or $TailP% so the Confidence Interval itself has $IntervalP% of the area.</p>
<p>&nbsp;</p>
<p>&nbsp;</p>
<p>&nbsp;</p>@
qu.5.4.editing=useHTML@
qu.5.4.solution=@
qu.5.4.algorithm=$Q=3;
$Pick=rint(3);
$CI=switch($Pick,"90","95","98");
$HalfTail=switch($Pick,0.05,0.025,0.01);
$HalfTailP=100*$HalfTail;
$Tail=2*$HalfTail;
$TailP=100*$Tail;
$IntervalP=100*(1-$Tail);
$Ans=$CI;
$Alt1=switch($Pick,"95","98","90");
$Alt2=switch($Pick,"98","90","95");
$Alt3=if(eq($Pick,0),"99",100*(1-$HalfTail));@
qu.5.4.uid=21825ee2-98a3-4119-ab07-15c6ed87073c@
qu.5.4.info=  Course=202;
  Type=MC;
@
qu.5.4.question=<div title="UW Statistics Bank/Confidence Intervals/Basics/Q3">Identify the confidence interval from the Normal distribution used in the figure below:
<p>&nbsp;</p>
<img hspace="4" title="The $IntervalP% Confidence Interval [IMG:ConfidenceInterval$IntervalP.gif]" alt="" src="__BASE_URI__CI/Basics/ConfidenceInterval$IntervalP.gif" halign="Center" /></div>@
qu.5.4.answer=1@
qu.5.4.choice.1=$Ans%@
qu.5.4.choice.2=$Alt1%@
qu.5.4.choice.3=$Alt2%@
qu.5.4.choice.4=$Alt3%@
qu.5.4.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&alpha;</mi></mrow></mstyle></math>%@
qu.5.4.fixed=@

qu.5.5.mode=True False@
qu.5.5.name=06. CI width@
qu.5.5.comment=<p>False, because the CI depends on the sample SD which can vary even with equal sample sizes and confidence levels.</p>@
qu.5.5.editing=useHTML@
qu.5.5.solution=@
qu.5.5.algorithm=@
qu.5.5.uid=77b58728-0496-4d76-be2c-9d36fcb94a61@
qu.5.5.info=  Course=202;
  Type=T/F;
  Algorithmic=no;
@
qu.5.5.question=<div title="UW Statistics Bank/Confidence Intervals/Basics/Q$6">The width of a confidence interval for a population mean that is based on the <em>t</em> distribution varies from sample to sample even if the sample size and confidence level is kept fixed.</div>@
qu.5.5.answer=1@
qu.5.5.choice.1=True@
qu.5.5.choice.2=False@
qu.5.5.fixed=@

qu.5.6.mode=True False@
qu.5.6.name=01. t distribution variance@
qu.5.6.comment=<p>If the degrees of freedom is <em>r</em>, then the variance is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>r</mi><mrow><mi>r</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>2</mn></mrow></mfrac></mrow></mstyle></math>which is >1 .</p>@
qu.5.6.editing=useHTML@
qu.5.6.solution=@
qu.5.6.algorithm=@
qu.5.6.uid=bb87c2cc-e37b-4d95-8e10-7ecc9d3b5c02@
qu.5.6.info=  Course=202;
  Type=T/F;
  Algorithmic=no;
@
qu.5.6.question=<div title="UW Statistics Bank/Confidence Intervals/Basics/Q01">The t-distribution has a variance that is greater than one.</div>@
qu.5.6.answer=1@
qu.5.6.choice.1=True@
qu.5.6.choice.2=False@
qu.5.6.fixed=@

qu.5.7.mode=Multiple Choice@
qu.5.7.name=07. CI & Proportion@
qu.5.7.comment=<p>The confidence interval is symmetric about its mean, so just take the midpoint of the two endpoints given:</p>
<p>Mean = <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mi mathvariant='normal'>$LHP</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$RHP</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$MP</mi></mrow></mstyle></math>and so the statement is $Ans.</p>@
qu.5.7.editing=useHTML@
qu.5.7.solution=@
qu.5.7.algorithm=$Q=7;
$LHP=range(9.5,24.5);
$RHP=range($LHP+2,$LHP+20);
$MP=($LHP+$RHP)/2;
$NMP=$MP+switch(rint(4),-0.5,-1,0.5,1);
$Pick=rint(2);
$Ans=switch($Pick,"True","False");
$NAns=switch($Pick,"False","True");
$Guess=switch($Pick,$MP,$NMP);@
qu.5.7.uid=c6381acb-f334-4fa3-adbc-07f58f68e70c@
qu.5.7.info=  Course=202;
  Type=MC;
@
qu.5.7.question=<div title="UW Statistics Bank/Confidence Intervals/Basics/Q$Q">A confidence interval was constructed around a proportion. The interval was from $LHP% to $RHP%. The proportion that was used to construct this interval was $Guess%.</div>@
qu.5.7.answer=1@
qu.5.7.choice.1=$Ans@
qu.5.7.choice.2=$NAns@
qu.5.7.fixed=@

