qu.1.topic=Normal Approximation@

qu.1.1.mode=Multiple Choice@
qu.1.1.name=02. Test Statistic II@
qu.1.1.comment=@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$Q=2;

$U1=range(70,90,1);
$U2=range(100,130,1);
$S1=range(40,70,1);
$S2=range(40,70,1);
$N1=range(50,100,1);
$N2=range(50,100,1);
$N=$N1+$N2;
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$U=$U2-$U1;
$ANS=decimal(3,$U/$S);
$ALT1=$ANS+range(1,2,0.01);
$ALT2=$ANS+range(2,3,0.01);
$ALT3=$ANS+range(1,2,0.01);@
qu.1.1.uid=900ce1fb-531f-45ac-ae62-067c060967ad@
qu.1.1.info=  Course=202;
  Type=MC;
@
qu.1.1.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two-Sample/Normal Approximation/Q$Q">In testing the equality of the two means below, what is the test statistic (in absolute value)?&nbsp;
<table cellspacing="0" cellpadding="4" bordercolor="#111111" border="0" id="AutoNumber1" style="border-collapse: collapse">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td align="center"><strong>Sample 1</strong></td>
            <td align="center"><strong>Sample 2</strong></td>
        </tr>
        <tr>
            <td><strong>Sample size</strong></td>
            <td align="center">$N1</td>
            <td align="center">$N2</td>
        </tr>
        <tr>
            <td><strong>Sample mean</strong></td>
            <td align="center">$U1</td>
            <td align="center">$U2</td>
        </tr>
        <tr>
            <td><strong>Sample standard deviation</strong></td>
            <td align="center">$S1</td>
            <td align="center">$S2</td>
        </tr>
    </tbody>
</table>
</div>@
qu.1.1.answer=1@
qu.1.1.choice.1=$ANS@
qu.1.1.choice.2=$ALT1@
qu.1.1.choice.3=$ALT2@
qu.1.1.choice.4=$ALT3@
qu.1.1.fixed=@

qu.1.2.mode=Multiple Choice@
qu.1.2.name=03. Runners@
qu.1.2.comment=@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$Q=3;
$U1=range(1400,1500);
$U2=range(1000,1300);
$N1=range(20,30);
$N2=range(20,30);
$S1=range(400,800);
$S2=range(300,900);
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$DF1=(($S1^2)/$N1+($S2^2)/$N2)^2;
$DF2=($S1^4)/(($N1^2)*($N1-1))+($S2^4)/(($N2^2)*($N2-1));
$DF=decimal(0,$DF1/$DF2);
$U=$U1-$U2;
$t=$U/$S;
$T1=maple("stats[statevalf,cdf,studentst[$DF]]($t)");
$PV=(1-$T1);
$ANS=if(le($PV,0.01),"Reject Null Hypothesis","Failed to Reject Null Hypothesis");
$ALT=if(ge($PV,0.01),"Reject Null Hypothesis","Failed to Reject Null Hypothesis");
$N=$N1+$N2;@
qu.1.2.uid=b2af1ebd-6c54-4d6d-9c41-afdaf67a87fe@
qu.1.2.info=  Course=202;
  Type=MC;
@
qu.1.2.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two-Sample/Normal Approximation/Q$Q">A running coach wanted to see whether runners ran faster after eating spaghetti the night before a race. $N&nbsp;random runners were chosen for this study. They ran a 5-kilometre race after having a normal dinner the night before, and then a week later, re-ran the same race after having a spaghetti dinner the night before. Their results (in seconds) are in the table below. At &alpha; = .01, does the data support the alternative hypothesis that runners do indeed run faster after eating?
<p>&nbsp;</p>
<table cellspacing="0" cellpadding="4" bordercolor="#111111" border="0" id="AutoNumber1" style="border-collapse: collapse">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td valign="top">Regular Dinner</td>
            <td valign="top">Spaghetti Dinner</td>
            <td>&nbsp;</td>
        </tr>
        <tr>
            <td>Sample mean</td>
            <td align="center">$U1</td>
            <td align="center">$U2</td>
            <td align="center">&nbsp;</td>
        </tr>
        <tr>
            <td>Sample standard deviation</td>
            <td align="center">$S1</td>
            <td align="center">$S2</td>
            <td align="center">&nbsp;</td>
        </tr>
    </tbody>
</table>
</div>
<p>&nbsp; Sample size&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$N1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $N2</p>@
qu.1.2.answer=3@
qu.1.2.choice.1=Inconclusive@
qu.1.2.choice.2=$ALT@
qu.1.2.choice.3=$ANS@
qu.1.2.fixed=@

qu.1.3.mode=Multiple Choice@
qu.1.3.name=01. Test Statistic 1@
qu.1.3.comment=@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$Q=1;
$U1=range(7,9,0.01);
$U2=range(10,13,0.01);
$S1=range(4,7,0.01);
$S2=range(4,7,0.01);
$N1=range(10,20);
$N2=range(10,20);
$N=$N1+$N2;
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$U=$U2-$U1;
$ANS=decimal(3,$U/$S);
$ALT1=$ANS+range(1,2,0.01);
$ALT2=$ANS+range(2,3,0.01);
$ALT3=$ANS+range(1,2,0.01);@
qu.1.3.uid=3abb752a-8728-4588-a8cb-700e252f04f3@
qu.1.3.info=  Type=MC;
  Course=202;
@
qu.1.3.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two-Sample/Normal Approximation/Q$Q">In testing the equality of the two means below, what is the test statistic (in absolute value)?<br />
<br />
<br />
<table cellspacing="0" cellpadding="4" bordercolor="#111111" border="0" id="AutoNumber1" style="border-collapse: collapse">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td align="center"><strong>Sample 1</strong></td>
            <td align="center"><strong>Sample 2</strong></td>
        </tr>
        <tr>
            <td><strong>Sample size</strong></td>
            <td align="center">$N1</td>
            <td align="center">$N2</td>
        </tr>
        <tr>
            <td><strong>Sample mean</strong></td>
            <td align="center">$U1</td>
            <td align="center">$U2</td>
        </tr>
        <tr>
            <td><strong>Sample standard deviation</strong></td>
            <td align="center">$S1</td>
            <td align="center">$S2</td>
        </tr>
    </tbody>
</table>
</div>@
qu.1.3.answer=4@
qu.1.3.choice.1=$ALT1@
qu.1.3.choice.2=$ALT2@
qu.1.3.choice.3=$ALT3@
qu.1.3.choice.4=$ANS@
qu.1.3.fixed=@

qu.2.topic=Student t@

qu.2.1.mode=Multiple Choice@
qu.2.1.name=05. Octane Booster II@
qu.2.1.comment=@
qu.2.1.editing=useHTML@
qu.2.1.solution=@
qu.2.1.algorithm=$Q=5;
$X1=range(20,30,0.01);
$X2=range(20,30,0.01);
$X3=range(20,30,0.01);
$X4=range(20,30,0.01);
$X5=range(20,30,0.01);
$X6=range(20,30,0.01);
$X7=range(20,30,0.01);
$X8=range(25,30,0.01);
$X9=range(25,30,0.01);
$X10=range(25,30,0.01);
$X11=range(25,30,0.01);
$X12=range(25,30,0.01);
$X13=range(25,30,0.01);
$X14=range(25,30,0.01);
$U1=($X1+$X2+$X3+$X4+$X5+$X6+$X7)/7;
$U2=($X8+$X9+$X10+$X11+$X12+$X13+$X14)/7;
$ANS=decimal(3,$U1-$U2);
$ALT1=decimal(3,$U2-$U1);
$ALT2=decimal(3,$U1/2);
$ALT3=decimal(3,$U2/2);@
qu.2.1.uid=25e0f389-b235-40ce-b74b-41de42b4a041@
qu.2.1.info=  Course=202;
  Type=MC;
@
qu.2.1.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two-Sample/Student t/Q$Q">A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster.<br />
<br />
<div>
<table cellspacing="0" bordercolor="#111111" border="0" style="border-collapse: collapse" id="AutoNumber1">
    <tbody>
        <tr>
            <td align="center"><strong>Miles / Gal <br />
            Without</strong></td>
            <td align="center"><strong>Miles / Gal <br />
            With</strong></td>
        </tr>
        <tr>
            <td align="center">$X1&nbsp;</td>
            <td align="center">$X8</td>
        </tr>
        <tr>
            <td align="center">$X2&nbsp;</td>
            <td align="center">$X9</td>
        </tr>
        <tr>
            <td align="center">$X3&nbsp;</td>
            <td align="center">$X10</td>
        </tr>
        <tr>
            <td align="center">$X4&nbsp;</td>
            <td align="center">$X11</td>
        </tr>
        <tr>
            <td align="center">$X5&nbsp;</td>
            <td align="center">$X12</td>
        </tr>
        <tr>
            <td align="center">$X6&nbsp;</td>
            <td align="center">$X13</td>
        </tr>
        <tr>
            <td align="center">$X7&nbsp;</td>
            <td align="center">$X14</td>
        </tr>
    </tbody>
</table>
</div>
<p>Determine the mean of the difference.</p>
</div>@
qu.2.1.answer=4@
qu.2.1.choice.1=$ALT1@
qu.2.1.choice.2=$ALT2@
qu.2.1.choice.3=$ALT2@
qu.2.1.choice.4=$ANS@
qu.2.1.fixed=@

qu.2.2.mode=Multiple Choice@
qu.2.2.name=14. Two Different Diets@
qu.2.2.comment=@
qu.2.2.editing=useHTML@
qu.2.2.solution=@
qu.2.2.algorithm=$Q="14";
$U1=range(14,15,0.1);
$U2=range(10,13,0.01);
$N1=range(7,11,1);
$N2=range(8,12,1);
$S1=range(4,8,0.1);
$S2=range(3,9,0.01);
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$DF1=(($S1^2)/$N1+($S2^2)/$N2)^2;
$DF2=($S1^4)/(($N1^2)*($N1-1))+($S2^4)/(($N2^2)*($N2-1));
$DF=decimal(0,$DF1/$DF2);
$U=$U1-$U2;
$t=$U/$S;
$T1=maple("stats[statevalf,cdf,studentst[$DF]]($t)");
$PV=2*(1-$T1);
$ANS=if(le($PV,0.05),"Reject Null Hypothesis","Failed to Reject Null Hypothesis");
$ALT1=if(ge($PV,0.05),"Reject Null Hypothesis","Failed to Reject Null Hypothesis");@
qu.2.2.uid=c4c2fa59-64f7-4637-9e8d-eceae470060d@
qu.2.2.info=  Type=MC;
  Course=202;
@
qu.2.2.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two Sample/Student t/Q$Q">Nutritional researchers conducted an investigation of two high-fiber diets intended to reduce cholesterol level. a group of people with high cholesterol were randomly selected to receive an "rice" diet or a "vegetable" diet for 20 days. Use t test to compare the diets at 5% significance level.
<p>Null Hypothesis: The means from two respective diets are the same</p>
<p>Alternative Hypothesis:&nbsp; The two means from the two diets differ.<br />
<br />
<table cellspacing="2" border="0">
    <tbody>
        <tr>
            <td align="center" colspan="4">Fall in Cholesterol (mg/dL)</td>
        </tr>
        <tr>
            <td>Diet</td>
            <td>n</td>
            <td>Mean</td>
            <td>SD</td>
        </tr>
        <tr>
            <td>Rice</td>
            <td>$N1</td>
            <td>&nbsp; $U1</td>
            <td>$S1</td>
        </tr>
        <tr>
            <td>Vegetable</td>
            <td>$N2</td>
            <td>&nbsp; $U2</td>
            <td>$S2</td>
        </tr>
    </tbody>
</table>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
</div>@
qu.2.2.answer=1@
qu.2.2.choice.1=$ANS@
qu.2.2.choice.2=$ALT1@
qu.2.2.fixed=@

qu.2.3.mode=Multiple Choice@
qu.2.3.name=06. Octane Booster III@
qu.2.3.comment=@
qu.2.3.editing=useHTML@
qu.2.3.solution=@
qu.2.3.algorithm=$Q="06";
$X1=range(20,30,0.01);
$X2=range(20,30,0.01);
$X3=range(20,30,0.01);
$X4=range(20,30,0.01);
$X5=range(20,30,0.01);
$X6=range(20,30,0.01);
$X7=range(20,30,0.01);
$X8=range(25,30,0.01);
$X9=range(25,30,0.01);
$X10=range(25,30,0.01);
$X11=range(25,30,0.01);
$X12=range(25,30,0.01);
$X13=range(25,30,0.01);
$X14=range(25,30,0.01);
$U1=($X1+$X2+$X3+$X4+$X5+$X6+$X7)/7;
$U2=($X8+$X9+$X10+$X11+$X12+$X13+$X14)/7;
$V1=(($X1-$U1)^2)+(($X2-$U1)^2)+(($X3-$U1)^2)+(($X4-$U1)^2)+(($X5-$U1)^2)+(($X6-$U1)^2)+(($X7-$U1)^2);
$V2=(($X8-$U2)^2)+(($X9-$U2)^2)+(($X10-$U2)^2)+(($X11-$U2)^2)+(($X12-$U2)^2)+(($X13-$U2)^2)+(($X14-$U2)^2);
$S=sqrt($V1/7+$V2/7);
$ANS=decimal(3,$S);
$ALT1=decimal(3,$S^2);
$ALT2=decimal(3,$S+range(1,4,0.1));
$ALT3=decimal(3,$U2/2);@
qu.2.3.uid=9f0b9684-c025-4751-a678-840508e47ab8@
qu.2.3.info=  Type=MC;
  Course=202;
@
qu.2.3.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two Sample/Student t/Q$Q">
A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster.
<p>&nbsp;</p>
<div>
<table cellspacing="0" bordercolor="#111111" border="0" style="border-collapse: collapse" id="AutoNumber1">
    <tbody>
        <tr>
            <td align="center"><strong>Miles / Gal <br />
            Without</strong></td>
            <td align="center"><strong>Miles / Gal <br />
            With</strong></td>
        </tr>
        <tr>
            <td align="center">$X1&nbsp;</td>
            <td align="center">$X8</td>
        </tr>
        <tr>
            <td align="center">$X2&nbsp;</td>
            <td align="center">$X9</td>
        </tr>
        <tr>
            <td align="center">$X3&nbsp;</td>
            <td align="center">$X10</td>
        </tr>
        <tr>
            <td align="center">$X4&nbsp;</td>
            <td align="center">$X11</td>
        </tr>
        <tr>
            <td align="center">$X5&nbsp;</td>
            <td align="center">$X12</td>
        </tr>
        <tr>
            <td align="center">$X6&nbsp;</td>
            <td align="center">$X13</td>
        </tr>
        <tr>
            <td align="center">$X7&nbsp;</td>
            <td align="center">$X14</td>
        </tr>
    </tbody>
</table>
</center></div>
<p>Determine the standard deviation&nbsp;of the difference.</p>
</div>@
qu.2.3.answer=4@
qu.2.3.choice.1=$ALT1@
qu.2.3.choice.2=$ALT2@
qu.2.3.choice.3=$ALT2@
qu.2.3.choice.4=$ANS@
qu.2.3.fixed=@

qu.2.4.mode=True False@
qu.2.4.name=08. Charity@
qu.2.4.comment=@
qu.2.4.editing=useHTML@
qu.2.4.solution=@
qu.2.4.algorithm=$Q=8;
$U1=range(14,15,0.1);
$U2=range(10,13,0.01);
$N1=range(7,11,1);
$N2=range(8,12,1);
$S1=range(4,8,0.1);
$S2=range(3,9,0.01);
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$DF1=(($S1^2)/$N1+($S2^2)/$N2)^2;
$DF2=($S1^4)/(($N1^2)*($N1-1))+($S2^4)/(($N2^2)*($N2-1));
$DF=decimal(0,$DF1/$DF2);
$N=$N1+$N2;
$U=$U1-$U2;
$t=$U/$S;
$T1=maple("stats[statevalf,cdf,studentst[$DF]]($t)");
$PV=(1-$T1);
$ANS=if(le($PV,0.01),"Reject Null Hypothesis","Failed to Reject Null Hypothesis");
$ALT1="Reject Null Hypothesis";@
qu.2.4.uid=1b6e579d-d0f1-404e-b0c5-e7e2961bd966@
qu.2.4.info=  Course=202;
  Type=T/F;
@
qu.2.4.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two-Sample/Student t/Q$Q">A local charity thinks that people in River Heights give more money to their charity than people in Lakeview. They conducted a survey of&nbsp;$N people in each subdivision and recorded the results. Let <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><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn mathvariant='italic'>0.01</mn></mrow></mstyle></math>&nbsp;
<p>&nbsp;</p>
<table cellspacing="0" cellpadding="4" bordercolor="#111111" border="0" style="border-collapse: collapse" id="AutoNumber1">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td align="center"><strong>River Heights</strong></td>
            <td align="center"><strong>Lakeview</strong></td>
        </tr>
        <tr>
            <td align="center"><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>x</mi></mrow><mi>&minus;</mi></mover></mrow></mstyle></math></td>
            <td align="center">\\$$U1</td>
            <td align="center">\\$$U2</td>
        </tr>
        <tr>
            <td align="center"><strong><em>s</em></strong></td>
            <td align="center">\\$$S1</td>
            <td align="center">\\$$S2</td>
        </tr>
        <tr>
            <td align="center"><strong><em>n</em></strong></td>
            <td align="center">$N1</td>
            <td align="center">$N2</td>
        </tr>
    </tbody>
</table>
<p>Is their hypothesis correct? i.e, is that true that there is enough evidence to support the claim that River Heights donates more money?</p>
</div>@
qu.2.4.answer=2@
qu.2.4.choice.1=True@
qu.2.4.choice.2=False@
qu.2.4.fixed=@

qu.2.5.mode=Multiple Choice@
qu.2.5.name=10. Blood Pressure@
qu.2.5.comment=@
qu.2.5.editing=useHTML@
qu.2.5.solution=@
qu.2.5.algorithm=@
qu.2.5.uid=6d852a76-4190-489f-ac33-75557641307d@
qu.2.5.info=  Course=202;
  Type=MC;
  Algorithmic=no;
@
qu.2.5.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two Sample/Student t/Q10">In a study comparing the systolic blood pressure of individuals sitting and standing, 10 subjects had their blood pressure measured in the two conditions. The investigator planned to test the hypothesis that the mean blood pressure readings are the same sitting and standing (the subjects remained in each position for 5 minutes). If the investigator tests at the 10% level of significance, the rejection region would be:</div>@
qu.2.5.answer=2@
qu.2.5.choice.1=| t |>1.734@
qu.2.5.choice.2=t < -1.833 or t > 1.8333@
qu.2.5.choice.3=| t |>1.725@
qu.2.5.choice.4=t > 1.8333@
qu.2.5.fixed=@

qu.2.6.mode=Multiple Choice@
qu.2.6.name=09. Single sided HT@
qu.2.6.comment=@
qu.2.6.editing=useHTML@
qu.2.6.solution=@
qu.2.6.algorithm=$Q=9;
$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(4,9,0.01);
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$DF1=(($S1^2)/$N1+($S2^2)/$N2)^2;
$DF2=($S1^4)/(($N1^2)*($N1-1))+($S2^4)/(($N2^2)*($N2-1));
$DF=decimal(0,$DF1/$DF2);
$U=$U1-$U2;
$t=$U/$S;
$T1=maple("stats[statevalf,cdf,studentst[$DF]]($t)");
$PV=(1-$T1);
$ANS=if(le($PV,0.1),"Reject Null Hypothesis","Fail to Reject Null 
Hypothesis");
$ALT=if(ge($PV,0.1),"Reject Null Hypothesis","Fail to Reject Null
Hypothesis");@
qu.2.6.uid=1ed3df94-65af-481c-9fd9-9f625237e9fc@
qu.2.6.info=  Course=202;
  Type=MC;
@
qu.2.6.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two-Sample/Student t/Q$Q">A real estate appraiser wanted to compare average apartment values in Waterloo and Kitchener. The table below shows the summarized data.
<p>&nbsp;</p>
<div align="center"><center>
<table cellspacing="3" cellpadding="3" bordercolor="#111111" border="0" style="border-collapse: collapse" id="AutoNumber1">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td>Kitchener</td>
            <td>Waterloo</td>
        </tr>
        <tr>
            <td>n</td>
            <td align="right">$N1&nbsp;</td>
            <td align="right">$N2</td>
        </tr>
        <tr>
            <td>y bar</td>
            <td align="right">$U1</td>
            <td align="right">$U2</td>
        </tr>
        <tr>
            <td>s</td>
            <td align="right">$S1</td>
            <td align="right">$S2</td>
        </tr>
    </tbody>
</table>
</center></div>
<p>Construct a t test to test the null hypothesis of no difference against the alternative that apartment values in Kitchener are higher than those in Waterloo. Use t test at 0.1 significance level. &nbsp;</p>
</div>@
qu.2.6.answer=1@
qu.2.6.choice.1=$ANS@
qu.2.6.choice.2=$ALT@
qu.2.6.fixed=@

qu.2.7.mode=Multiple Choice@
qu.2.7.name=03. Test Statistic?@
qu.2.7.comment=@
qu.2.7.editing=useHTML@
qu.2.7.solution=@
qu.2.7.algorithm=$Q=3;
$U1=range(7,9,0.01);
$U2=range(10,13,0.01);
$S1=range(4,7,0.01);
$S2=range(4,7,0.01);
$N1=range(10,20,1);
$N2=range(10,20,1);
$N=$N1+$N2;
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$U=$U2-$U1;
$ANS=decimal(3,$U/$S);
$ALT1=$ANS+range(1,2,0.01);
$ALT2=$ANS+range(2,3,0.01);
$ALT3=$ANS+range(1,2,0.01);@
qu.2.7.uid=29cc23bc-80d4-41b6-b18f-25e9a472a8d2@
qu.2.7.info=  Course=202;
  Type=MC;
@
qu.2.7.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two-Sample/Student t/Q$Q">The Excellent Drug Company claims its aspirin tablets will relieve headaches faster than any other aspirin on the market. To determine whether Excellent&rsquo;s claim is valid, random samples of sizes $N1 and $N2&nbsp;are chosen from aspirins made by Excellent and the Simple Drug Company. An aspirin is given to each of the&nbsp;$N randomly selected persons suffering from headaches and the number of minutes required for each to recover from the headache is recorded. The sample results are: <br />
<p>
<table cellspacing="1" cellpadding="3" border="0" id="AutoNumber1">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td>&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>X</mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&minus;</mo></mrow></mover><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math></td>
            <td>&nbsp; s</td>
        </tr>
        <tr>
            <td>Excellent (E)</td>
            <td>$U1</td>
            <td>&nbsp;$S1</td>
        </tr>
        <tr>
            <td>Simple (S)</td>
            <td>$U2</td>
            <td>&nbsp;$S2</td>
        </tr>
    </tbody>
</table>
</p>
<p>A 5% significance level test is performed to determine whether Excellent&rsquo;s aspirin cures headaches significantly faster than Simple&rsquo;s aspirin.&nbsp; The absolute value of the calculated value of the appropriate test statistic is:</p>
</div>@
qu.2.7.answer=3@
qu.2.7.choice.1=$ALT1@
qu.2.7.choice.2=$ALT2@
qu.2.7.choice.3=$ANS@
qu.2.7.choice.4=$ALT3@
qu.2.7.fixed=@

qu.2.8.mode=Multiple Choice@
qu.2.8.name=07. Wage parity@
qu.2.8.comment=@
qu.2.8.editing=useHTML@
qu.2.8.solution=@
qu.2.8.algorithm=$Q="07";
$Corp=switch(rint(4),"Donaldson","A123","Dugong","Anderson");
$U1=range(14,15,0.1);
$U2=range(10,13,0.01);
$N1=range(7,11,1);
$N2=range(8,12,1);
$S1=range(4,8,0.1);
$S2=range(3,9,0.01);
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$DF1=(($S1^2)/$N1+($S2^2)/$N2)^2;
$DF2=($S1^4)/(($N1^2)*($N1-1))+($S2^4)/(($N2^2)*($N2-1));
$DF=decimal(0,$DF1/$DF2);
$U=$U1-$U2;
$t=$U/$S;
$T1=maple("stats[statevalf,cdf,studentst[$DF]]($t)");
$PV=2*(1-$T1);
$ANS=if(le($PV,0.01),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT1=if(ge($PV,0.01),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.2.8.uid=b690d8a3-370e-49a4-a524-ad498b5f6431@
qu.2.8.info=  Type=MC;
  Course=202;
@
qu.2.8.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two Sample/Q$Q">$Corp Corporation wants to hire a temporary secretary. There are two employment agencies in town, and it is believed that the average hourly wages charged by both agencies are the same. Test this claim at a &alpha; = 0.01 .
<p>&nbsp;</p>
<table cellspacing="0" cellpadding="5" bordercolor="#111111" border="0" id="AutoNumber1" style="border-collapse: collapse">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td align="center">Agency A</td>
            <td align="center">Agency B</td>
        </tr>
        <tr>
            <td><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>x</mi></mrow><mi>&minus;</mi></mover></mrow></mstyle></math></td>
            <td align="center">\\$$U1</td>
            <td align="center">\\$$U2</td>
        </tr>
        <tr>
            <td align="center"><em>s</em></td>
            <td align="center">\\$$S1</td>
            <td align="center">\\$$S2</td>
        </tr>
        <tr>
            <td align="center"><em>n</em></td>
            <td align="center">$N1</td>
            <td align="center">$N2</td>
        </tr>
    </tbody>
</table>
</div>@
qu.2.8.answer=1@
qu.2.8.choice.1=$ANS@
qu.2.8.choice.2=$ALT1@
qu.2.8.fixed=@

qu.2.9.mode=Multiple Choice@
qu.2.9.name=13. Runners@
qu.2.9.comment=@
qu.2.9.editing=useHTML@
qu.2.9.solution=@
qu.2.9.algorithm=$Q=13;
$U1=range(14,15,0.1);
$U2=range(10,13,0.01);
$N1=range(7,11,1);
$N2=range(8,12,1);
$S1=range(4,8,0.1);
$S2=range(3,9,0.01);
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$DF1=(($S1^2)/$N1+($S2^2)/$N2)^2;
$DF2=($S1^4)/(($N1^2)*($N1-1))+($S2^4)/(($N2^2)*($N2-1));
$DF=decimal(0,$DF1/$DF2);
$U=$U2-$U1;
$t=$U/$S;
$T1=maple("stats[statevalf,cdf,studentst[$DF]]($t)");
$PV=2*(1-$T1);
$ANS=decimal(3,$t);
$ALT1=decimal(3,-$t);
$ALT2=decimal(3,$t/2);
$ALT3=decimal(3,$t+2);
$N=$N1+$N2;@
qu.2.9.uid=f4518333-20dc-4179-8ee8-7959e833fc31@
qu.2.9.info=  Course=202;
  Type=MC;
@
qu.2.9.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two-Sample/Student t/Q$Q">A running coach wanted to see whether runners ran faster after eating spaghetti the night before a race.&nbsp;$N random runners were chosen for this study. They ran a 5-kilometre race after having a normal dinner the night before, and then a week later, re-ran the same race after having a spaghetti dinner the night before. Their results (in seconds) are in the table below. At &alpha; = .01, what is the test value for this test?<br />
&nbsp;
<table cellspacing="0" cellpadding="4" bordercolor="#111111" border="0" style="border-collapse: collapse" id="AutoNumber1">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td valign="top">Regular Dinner</td>
            <td valign="top">Spaghetti Dinner</td>
            <td>&nbsp;</td>
        </tr>
        <tr>
            <td>Sample mean</td>
            <td align="center">$U1</td>
            <td align="center">$U2</td>
            <td align="center">&nbsp;</td>
        </tr>
        <tr>
            <td>Sample standard deviation</td>
            <td align="center">$S1</td>
            <td align="center">$S2</td>
            <td align="center">&nbsp;</td>
        </tr>
        <tr>
            <td>Sample size&nbsp;</td>
            <td align="center">$N1</td>
            <td align="center">$N2</td>
            <td align="center">&nbsp;</td>
        </tr>
    </tbody>
</table>
</div>
<p>&nbsp;</p>@
qu.2.9.answer=4@
qu.2.9.choice.1=$ALT1@
qu.2.9.choice.2=$ALT2@
qu.2.9.choice.3=$ALT3@
qu.2.9.choice.4=$ANS@
qu.2.9.fixed=@

qu.2.10.mode=Multiple Choice@
qu.2.10.name=01. Best hypothesis?@
qu.2.10.comment=@
qu.2.10.editing=useHTML@
qu.2.10.solution=@
qu.2.10.algorithm=@
qu.2.10.uid=4fa3c6e2-3d54-4a9f-9b1d-78a1c4ed706b@
qu.2.10.info=  Course=202;
  Type=MC;
  Algorithmic=no;
@
qu.2.10.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two-Sample/Student t/Q1">The Excellent Drug Company claims its aspirin tablets will relieve headaches faster than any other aspirin on the market. To determine whether Excellent&rsquo;s claim is valid, random samples of size 15 are chosen from aspirins made by Excellent and the Simple Drug Company. An aspirin is given to each of the 30 randomly selected persons suffering from headaches and the number of minutes required for each to recover from the headache is recorded. The sample results are:
<p>&nbsp;</p>
<p>
<table cellspacing="1" cellpadding="3" border="0" id="AutoNumber1">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td>&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>X</mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&minus;</mo></mrow></mover><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math></td>
            <td>&nbsp;s<sup>2</sup></td>
        </tr>
        <tr>
            <td>Excellent (E)</td>
            <td>8.4</td>
            <td>4.2</td>
        </tr>
        <tr>
            <td>Simple (S)</td>
            <td>8.9</td>
            <td>4.6</td>
        </tr>
    </tbody>
</table>
</p>
<p>A 5% significance level test is performed to determine whether Excellent&rsquo;s aspirin cures headaches significantly faster than Simple&rsquo;s aspirin. The appropriate hypothesis to be tested is:</p>
</div>@
qu.2.10.answer=3@
qu.2.10.choice.1=H: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> = 0 A: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> &gt; 0@
qu.2.10.choice.2=H: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> = 0 A: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> &ne; 0@
qu.2.10.choice.3=H: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> = 0 A: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> &lt; 0@
qu.2.10.choice.4=H: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> &lt; 0 A: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> = 0@
qu.2.10.choice.5=H: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> &gt; 0 A: &mu;<sub>E</sub> &minus; &mu;<sub>S</sub> = 0@
qu.2.10.fixed=@

qu.2.11.mode=Multiple Choice@
qu.2.11.name=02. Jewellery buying@
qu.2.11.comment=@
qu.2.11.editing=useHTML@
qu.2.11.solution=@
qu.2.11.algorithm=$Q=2;
$U1=range(14,15,0.1);
$U2=range(10,13,0.01);
$N1=range(7,11);
$N2=range(8,12);
$S1=range(1,3,0.1);
$S2=range(4,9,0.01);
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$DF1=(($S1^2)/$N1+($S2^2)/$N2)^2;
$DF2=($S1^4)/(($N1^2)*($N1-1))+($S2^4)/(($N2^2)*($N2-1));
$DF=decimal(0,$DF1/$DF2);
$U=$U1-$U2;
$t=$U/$S;
$T1=maple("stats[statevalf,cdf,studentst[$DF]]($t)");
$PV=(1-$T1);
$ANS=if(le($PV,0.01),"Yes","No");
$ALT=if(ge($PV,0.01),"Yes","No");@
qu.2.11.uid=afd313c7-faa3-4fab-aaef-94e92a053760@
qu.2.11.info=  Course=202;
  Type=MC;
@
qu.2.11.question=<div title="UW Statistics Bank/Hypothesis Testing/Two-Sample/Student t/Q$Q">A marketing firm asked a random set of married women and married men how much they were willing to spend for jewellery as a present for their spouse. Can the firm conclude, at &alpha;&nbsp; = .01, that each of the two groups has a different willingness to spend? (Use the unequal variances formula.)
<table cellspacing="0" cellpadding="4" bordercolor="#111111" border="0" id="AutoNumber1" style="border-collapse: collapse">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td align="center"><strong>Women</strong></td>
            <td align="center"><strong>Men</strong></td>
        </tr>
        <tr>
            <td><strong>Sample size</strong></td>
            <td align="center">$N1</td>
            <td align="center">$N2</td>
        </tr>
        <tr>
            <td><strong>Mean spending amount</strong></td>
            <td align="center">$U1</td>
            <td align="center">$U2</td>
        </tr>
        <tr>
            <td><strong>Sample standard deviation</strong></td>
            <td align="center">$S1</td>
            <td align="center">$S2</td>
        </tr>
    </tbody>
</table>
</div>@
qu.2.11.answer=2@
qu.2.11.choice.1=$ALT@
qu.2.11.choice.2=$ANS@
qu.2.11.fixed=@

qu.2.12.mode=Multiple Choice@
qu.2.12.name=12. Apples browning@
qu.2.12.comment=@
qu.2.12.editing=useHTML@
qu.2.12.solution=@
qu.2.12.algorithm=$Q="12";
$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(4,8,0.1);
$S2=range(3,9,0.01);
$S=sqrt(($S1^2)/$N1+($S2^2)/$N2);
$DF1=(($S1^2)/$N1+($S2^2)/$N2)^2;
$DF2=($S1^4)/(($N1^2)*($N1-1))+($S2^4)/(($N2^2)*($N2-1));
$DF=decimal(0,$DF1/$DF2);
$U=$U1-$U2;
$t=$U/$S;
$T1=maple("stats[statevalf,cdf,studentst[$DF]]($t)");
$PV=2*(1-$T1);
$ANS=if(le($PV,0.05),"True","False");
$ALT1=if(ge($PV,0.05),"True","False");
$N=$N1+$N2;@
qu.2.12.uid=52f7450f-7a7c-4129-adcb-866a03397994@
qu.2.12.info=  Type=MC;
  Course=202;
@
qu.2.12.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two Sample/Student t/Q$Q"><img hspace="4" align="$Align" title="Apple [IMG:Apple$Which.gif]" alt="Apple" src="__BASE_URI__HT/TwoSample/Student_t/Apple$Which.gif" />A dietician investigated whether apples turned brown at different rates when exposed to air after being washed in hot water or in cold water. She took&nbsp;$N random apples and cut each in half. She washed&nbsp;$N1 apples in hot water and the others in cold water, and then put both different groups of apples&nbsp;out in a tray. Her results (in hours until turning a particular shade of brown) are in the table below.
<p>&nbsp;True or False: At &alpha; = .05, she saw a difference between the two treatments.</p>
<p>
<table cellspacing="0" cellpadding="4" bordercolor="#111111" border="0" style="border-collapse: collapse" id="AutoNumber1">
    <tbody>
        <tr>
            <td>&nbsp;</td>
            <td valign="top">Hot Water</td>
            <td valign="top">Cold Water</td>
            <td>&nbsp;</td>
        </tr>
        <tr>
            <td>Sample mean</td>
            <td align="center">$U1</td>
            <td align="center">$U2</td>
            <td align="center">&nbsp;</td>
        </tr>
        <tr>
            <td>Sample standard deviation</td>
            <td align="center">$S1</td>
            <td align="center">$S2</td>
            <td align="center">&nbsp;</td>
        </tr>
        <tr>
            <td>Sample size</font></td>
            <td align="center">$N1</font></td>
            <td align="center">$N2</font></td>
            <td align="center">&nbsp;</td>
        </tr>
    </tbody>
</table>
</p>
</div>
<p>&nbsp;</p>@
qu.2.12.answer=1@
qu.2.12.choice.1=$ANS@
qu.2.12.choice.2=$ALT1@
qu.2.12.fixed=@

qu.2.13.mode=Multiple Choice@
qu.2.13.name=04. Octane Booster I@
qu.2.13.comment=@
qu.2.13.editing=useHTML@
qu.2.13.solution=@
qu.2.13.algorithm=@
qu.2.13.uid=99d3ddba-51b3-4332-95da-ac60d3239990@
qu.2.13.info=  Course=202;
  Type=MC;
  Algorithmic=no;
@
qu.2.13.question=<div title="UW Statistics Bank/Hypothesis Testing/Two-Sample/Student t/Q4">A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster.
<p>&nbsp;</p>
<div>
<table cellspacing="0" bordercolor="#111111" border="0" style="border-collapse: collapse" id="AutoNumber1">
    <tbody>
        <tr>
            <td align="center"><strong>Miles / Gal <br />
            Without</strong></td>
            <td align="center"><strong>Miles / Gal <br />
            With</strong></td>
        </tr>
        <tr>
            <td align="center">21.2</td>
            <td align="center">23.8</td>
        </tr>
        <tr>
            <td align="center">25.4</td>
            <td align="center">25.6</td>
        </tr>
        <tr>
            <td align="center">20.9</td>
            <td align="center">22.4</td>
        </tr>
        <tr>
            <td align="center">27.6</td>
            <td align="center">28.3</td>
        </tr>
        <tr>
            <td align="center">22.8</td>
            <td align="center">24.5</td>
        </tr>
        <tr>
            <td align="center">27.3</td>
            <td align="center">28.8</td>
        </tr>
        <tr>
            <td align="center">23.4</td>
            <td align="center">25.2</td>
        </tr>
    </tbody>
</table>
</div>
<p>Let <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></mrow><mrow><msub><mi></mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub></mrow></mstyle></math> denote the difference in means between the case where the car is driven without a booster and otherwise.</p>
<p>Select the alternative hypothesis:</p>
</div>@
qu.2.13.answer=3@
qu.2.13.choice.1=<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><msub><mi>H</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><msub><mi>&mu;</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>0</mn></mrow></mstyle></math>@
qu.2.13.choice.2=<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><msub><mi>H</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><msub><mi>&mu;</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&gt;</mo><mn>0</mn></mrow></mstyle></math>@
qu.2.13.choice.3=<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><msub><mi>H</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><msub><mi>&mu;</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mn>0</mn></mrow></mstyle></math>@
qu.2.13.choice.4=<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><msub><mi>H</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><msub><mi>&mu;</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub><mrow><mo lspace='0.0em' rspace='0.0em'>&ne;</mo></mrow><mn>0</mn></mrow></mstyle></math>@
qu.2.13.fixed=@

qu.2.14.mode=Multiple Choice@
qu.2.14.name=11. Psych vs Biology grades@
qu.2.14.comment=@
qu.2.14.editing=useHTML@
qu.2.14.solution=@
qu.2.14.algorithm=$Q="11";
$U1=range(9,15,0.01);
$U2=range(5,8,0.01);
$N1=range(10,20,1);
$N2=range(10,20,1);@
qu.2.14.uid=87a013ae-0f28-4d09-96cc-cd1bbdc6fd3b@
qu.2.14.info=  Type=MC;
  Course=202;
@
qu.2.14.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Two Sample/Student t/Q$Q">A college class believes that the average grade of psychology students and the average grade of biology students are different. The class found that the grade averages of a sample of $N1&nbsp;psychology students was $U1, and the average grade of a sample of&nbsp;$N2 biology students was $U2. What is the null hypothesis for this study?</div>@
qu.2.14.answer=4@
qu.2.14.choice.1=<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><msub><mi>H</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><mi>&mu;</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn mathvariant='italic'>3.2</mn><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mo mathvariant='bold-italic' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&#32;</mo><mn mathvariant='italic'>2.9</mn></mrow></mstyle></math>@
qu.2.14.choice.2=<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><msub><mi>H</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><msub><mi>&mu;</mi><mrow><mi>psychology</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>3.2</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msub><mi>H</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><msub><mi>&mu;</mi><mrow><mi>biology</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>2.9</mn></mrow></mstyle></math>@
qu.2.14.choice.3=<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><msub><mi>H</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><msub><mi>&mu;</mi><mrow><mi>psychology</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msub><mi>&mu;</mi><mrow><mi>biology</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>6.1</mn></mrow></mstyle></math>@
qu.2.14.choice.4=<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><msub><mi>H</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><msub><mi>&mu;</mi><mrow><mi>psychology</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>&mu;</mi><mrow><mi>biology</mi></mrow></msub></mrow></mstyle></math>@
qu.2.14.fixed=@

