qu.1.topic=Normal Approximation@

qu.1.1.mode=Multiple Choice@
qu.1.1.name=04. NCAA@
qu.1.1.comment=@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$Q=04;
$Which=rint(4);
$Align=switch(rint(2),"Left","Right");
$U=range(103,105,0.1);
$S=range(16,18,0.01);
$Xbar=range(101,103,0.01);
$N=range(50,60,1);
$T=($Xbar-$U)/($S/sqrt($N));
$Z=maple("stats[statevalf,icdf,normald](0.01)");
$ANS=if(le($T,$Z),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT=if(ge($T,$Z),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.1.1.uid=daaee5e2-8a5e-4c50-adc3-31f621946e9e@
qu.1.1.info=  Course=202;
  Keyword=biology;
  Type=MC;
@
qu.1.1.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">
<img hspace="4" align="$Align" title="Football [IMG:Football$Which.gif]" alt="Football" src="__BASE_URI__HT/OneSample/Football$Which.gif" />A paper reported on physical characteristics of Division I starting football players in the 1988 football season. Information for teams ranked in the top 20 was easily obtained, and it was reported that the mean weight of starters on top 20 teams was $U kg. A sample of $N starting players from division I teams that were not ranked in the top 20 resulted in a sample mean weight of $Xbar kg and a sample standard deviation of $S kg.
<p><span style="vertical-align: -5px;">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></mstyle></math></span><span style="vertical-align: -5px;">=true mean weight of starters on teams that are not ranked in the top 20.</span></p>
&nbsp;H<sub>0</sub>: <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></mstyle></math>= $U&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></mstyle></math>< $U
<p><br />
Is there sufficient evidence to conclude that the mean weight for  non-top 20 starters is less than $U, the known value for top 20 teams?  Assume normality.(<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&alpha;</mi></mrow></mstyle></math> = 0.01)</p>
</div>@
qu.1.1.answer=1@
qu.1.1.choice.1=$ANS@
qu.1.1.choice.2=$ALT@
qu.1.1.fixed=@

qu.1.2.mode=Multiple Choice@
qu.1.2.name=05. IQ@
qu.1.2.comment=@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$Q=5;
$U=range(100,101,0.01);
$S=range(16,18,0.01);
$Xbar=range(101,102,0.01);
$N=range(50,60,1);
$T=($Xbar-$U)/($S/sqrt($N));
$Z=maple("stats[statevalf,cdf,normald]($T)");
$PV=1-$Z;
$ANS=if(le($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");@
qu.1.2.uid=4cb15c21-add9-406a-ad20-a3921d6ada29@
qu.1.2.info=  Course=202;
  Keyword=biology;
  Type=MC;
@
qu.1.2.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">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></mstyle></math>denote the true average IQ for children in a certain region of Canada. The average IQ for $N children in Canada is $U with standard deviation of $S.&nbsp; Education authorities are interested in testing . Assume normality.(<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> = 0.01)
<p>&nbsp;</p>
<p>H<sub>0</sub>: <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></mstyle></math>= $U&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></mstyle></math>> $U</p>
<p><span style="vertical-align: -5px;"><br />
</span></p>
</div>@
qu.1.2.answer=1@
qu.1.2.choice.1=$ANS@
qu.1.2.choice.2=$ALT@
qu.1.2.fixed=@

qu.1.3.mode=Multiple Choice@
qu.1.3.name=10. College Attendance@
qu.1.3.comment=@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$Q=10;
$From=switch(rint(4),"Eastern Canada","Ontario","Quebec","Western Canada");
$U1=range(0.3,0.35,0.001);
$N=range(200,250);
$U=100*$U1;
$n=range(80,90);
$P=$n/$N;
$S=sqrt($U1*(1-$U1)/$N);
$T=($P-$U1)/$S;
$Z=maple("stats[statevalf,cdf,normald]($T)");
$PV=1-$Z;
$ANS=if(le($PV,0.01),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT=if(ge($PV,0.01),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.1.3.uid=4bfdd993-e2e5-44eb-8012-444d2bedceda@
qu.1.3.info=  Course=202;
  Type=MC;
  Keyword=biology;
@
qu.1.3.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">The <em>National Post </em>reported that $U% of all adult Canadians have attended at least 1 year of college. Suppose that a random sample of $N adults in $From included $n with one or more years of college were taken.&nbsp; <br />
<br />
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></mstyle></math>be the true proportion of all adult Canadians have attended at least one year of college.<br />
<br />
Note: data does not represent reality. This is just for illustration purposes.
<p>H<sub>0</sub>: <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></mstyle></math>= $U1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></mstyle></math>> $U1</p>
<p><br />
Does this data support the assertion that a higher proportion of people  from $From (as compared to&nbsp;Canada as a whole) have attended at least one  year of college? Assume normality(<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&alpha;</mi></mrow></mstyle></math> = 0.01)</p>
</div>@
qu.1.3.answer=1@
qu.1.3.choice.1=$ANS@
qu.1.3.choice.2=$ALT@
qu.1.3.fixed=@

qu.1.4.mode=Multiple Choice@
qu.1.4.name=03. Test Anxiety@
qu.1.4.comment=@
qu.1.4.editing=useHTML@
qu.1.4.solution=@
qu.1.4.algorithm=$Q=3;
$U=range(40,42,0.01);
$S=range(10,12,0.01);
$Xbar=range(42,43,0.01);
$N=range(50,60,1);
$T=($Xbar-$U)/($S/sqrt($N));
$Z=maple("stats[statevalf,cdf,normald]($T)");
$PV=1-$Z;
$ANS=if(le($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT=if(ge($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.1.4.uid=6aaf29e1-a699-4e0c-851c-f3c103cd57c7@
qu.1.4.info=  Course=202;
  Keyword=biology;
@
qu.1.4.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">Almost every student has experienced some degree of test anxiety at one time or another. It was hypothesized that students in countries where high-school testing had important consequences in terms of future opportunities (such as Japan) would experience a greater level of test anxiety than do students in Canada. Test-anxiety scores were recorded for a sample of Japanese high school students. For this sample <br />
<p>&nbsp;&nbsp; n = $N&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; X Bar = $Xbar&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; s = $S&nbsp;</p>
<p>For Canadian high school students, the mean test anxiety score is thought to be $U.</p>
<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></mstyle></math>= true mean test anxiety score for Japanese high school students.</p>
<p>H<sub>0</sub>: <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></mstyle></math>= $U&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></mstyle></math>> $U</p>
<p>Does the sample data support the researcher's theory? Assume normality. (<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&alpha;</mi></mrow></mstyle></math> = 0.05)<span style="vertical-align: -5px;"><br />
</span></p>
</div>@
qu.1.4.answer=1@
qu.1.4.choice.1=$ANS@
qu.1.4.choice.2=$ALT@
qu.1.4.fixed=@

qu.1.5.mode=Multiple Choice@
qu.1.5.name=01. Sodium Study: Test Statistic@
qu.1.5.comment=@
qu.1.5.editing=useHTML@
qu.1.5.solution=@
qu.1.5.algorithm=$Q=1;
$Align=switch(rint(2),"Left","Right");
$Which=1+rint(4);
$U=range(3000,3500,25);
$S=range(1000,1500,10);
$Xbar=range(3500,4000,25);
$N=range(100,150,5);
$T=($Xbar-$U)/($S/sqrt($N));
$ANS=decimal(3,$T);
$ALT1=decimal(3,($Xbar-$U)/($S));
$ALT2=decimal(3,$ANS+range(1,4,0.1));
$ALT3=decimal(3,$ANS+range(1,4,0.1));@
qu.1.5.uid=a9c80ce5-5e84-4b2f-b36e-8f93e5731cc0@
qu.1.5.info=  Course=202;
  Keyword=biology;
  Course=232;
@
qu.1.5.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">
<img hspace="4" align="$Align" alt="Salt" src="__BASE_URI__HT/OneSample/Salt$Which.gif" />The Food and Nutrition Board of the National Academy of Sciences reports that the mean daily sodium intake should not exceed $U mg. In a study of sodium intake, a sample of U.S residents was found to have a mean daily sodium intake of $Xbar. Suppose that this result was based on a sample of size $N and that the population standard deviation is $S mg. The reserachers were interested in determining whether the mean daily sodium intake for U.S residents exceeded the maximum recommended level. 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></mstyle></math>represent the true mean sodium intake for all U.S residents. Then, <br />
<p>H<sub>0</sub>: <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></mstyle></math>= $U&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></mstyle></math>> $U</p>
<p>What is the test statistic?</p>
</div>@
qu.1.5.answer=1@
qu.1.5.choice.1=$ANS@
qu.1.5.choice.2=$ALT1@
qu.1.5.choice.3=$ALT2@
qu.1.5.choice.4=$ALT3@
qu.1.5.fixed=@

qu.1.6.mode=Multiple Choice@
qu.1.6.name=02. Lead Effects on Mental Health@
qu.1.6.comment=@
qu.1.6.editing=useHTML@
qu.1.6.solution=@
qu.1.6.algorithm=$Q=2;
$U=range(14,15,0.01);
$S=range(5,10,0.01);
$Xbar=range(15,16,0.01);
$N=range(40,50,1);
$T=($Xbar-$U)/($S/sqrt($N));
$Z=maple("stats[statevalf,cdf,normald]($T)");
$PV=1-$Z;
$ANS=if(le($PV,0.01),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT=if(ge($PV,0.01),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.1.6.uid=29052b2c-c8d8-46f4-971b-08f539851a71@
qu.1.6.info=  Course=202;
  Keyword=biology;
@
qu.1.6.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">In recent years, a substantial amount of research has focused on a possible relationship between chemical contamination of various sorts and mental retardation. An article reported data on hair-lead concentration for a sample of mentally retarded children for which the cause of retardation was unknown. Summary quantities were <br />
<p>&nbsp;&nbsp; n = $N&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; X Bar = $Xbar ppm&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; s = $S ppm</p>
<p>The paper states that $U ppm is considered the acceptable upper limit of hair-lead concentration.</p>
<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></mstyle></math>= the average hair-lead concentration for all mentally retarded children with the cause of retardation unknown.&nbsp;</p>
<p>H<sub>0</sub>:&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></mrow></mstyle></math> = $U &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>:&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></mrow></mstyle></math> > $U&nbsp;&nbsp; at 0.01 significance level</p>
<p>Does the given sample data support the research hypothesis that true  average hair concentration for all such mentally retarded chidren  exceeds the acceptable upper limit? Assume normality.</p>
</div>@
qu.1.6.answer=1@
qu.1.6.choice.1=$ANS@
qu.1.6.choice.2=$ALT@
qu.1.6.fixed=@

qu.1.7.mode=Multiple Choice@
qu.1.7.name=08. Environment@
qu.1.7.comment=@
qu.1.7.editing=useHTML@
qu.1.7.solution=@
qu.1.7.algorithm=$Q=8;
$U1=range(0.1,0.13,0.001);
$N=range(200,250,1);
$U=100*$U1;
$n=range(30,35,1);
$P=$n/$N;
$S=sqrt($U1*(1-$U1)/$N);
$T=($P-$U1)/$S;
$Z=maple("stats[statevalf,cdf,normald]($T)");
$PV=2*(1-$Z);
$ANS=if(le($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT=if(ge($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.1.7.uid=e74bb882-d00c-4e3d-b93e-9efb889679b0@
qu.1.7.info=  Course=202;
  Type=MC;
@
qu.1.7.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">Environment problems associated with leaded gasolines are well known. Many motorists have tampered with their cars emission-control devices in order to save money by purchasing leaded rather than unleaded gas. It was reported that $U% of all Ontarian motorists have engaged in such tampering. Suppose that after obtaining a random sample of $N cars from one particular region in Ontario, the emission-control devices of $n of them are found to have been modified.&nbsp; 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></mstyle></math>denote the proportion of cars in this country with modified emission-control devices.
<p>H<sub>0</sub>: <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></mstyle></math>= $U1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></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><mo lspace='0.0em' rspace='0.0em'>&ne;</mo></mrow></mstyle></math> $U1</p>
<p><strong>Does this suggest that the proportion of cars in this country with tampered devices differs from the province-wide proportion?</strong>&nbsp;&nbsp; Assume normality. (<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&alpha;</mi></mrow></mstyle></math> = 0.05)</p>
</div>@
qu.1.7.answer=1@
qu.1.7.choice.1=$ANS@
qu.1.7.choice.2=$ALT@
qu.1.7.fixed=@

qu.1.8.mode=Multiple Choice@
qu.1.8.name=07. Blood Pressure@
qu.1.8.comment=@
qu.1.8.editing=useHTML@
qu.1.8.solution=@
qu.1.8.algorithm=$Q=7;
$U=range(126,128,0.01);
$S=range(6,8,0.01);
$Xbar=range(128,129,0.01);
$N=range(50,60,1);
$T=($Xbar-$U)/($S/sqrt($N));
$Z=maple("stats[statevalf,cdf,normald]($T)");
$PV=2*(1-$Z);
$ANS=decimal(3,$PV);
$ALT1=decimal(3,1-$Z);
$ALT2=decimal(3,$Z);
$ALT3=decimal(3,0.01);@
qu.1.8.uid=da05e36b-a19f-4a03-a4f7-b03ba7262dc9@
qu.1.8.info=  Type=MC;
  Course=202;
  Keyword=biology;
@
qu.1.8.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">The mean systolic blood pressure for white males aged 35-44 in Canada is $U. A report said that the mean blood pressure and standard deviation of a sample of $N diabetic males aged 35-44 are $Xbar and $S, respectively. 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></mstyle></math>denote the true mean systolic blood pressure for diabetic males aged 35-44
<p>H<sub>0</sub>: <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></mstyle></math>= $U&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></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><mo lspace='0.0em' rspace='0.0em'>&ne;</mo></mrow></mstyle></math> $U</p>
<p>What is the p-value? Assume normality. (<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&alpha;</mi></mrow></mstyle></math> = 0.01)</p>
<p>&nbsp;</p>
<p><span style="vertical-align: -5px"><br />
</span></p>
</div>@
qu.1.8.answer=1@
qu.1.8.choice.1=$ANS@
qu.1.8.choice.2=$ALT1@
qu.1.8.choice.3=$ALT2@
qu.1.8.choice.4=$ALT3@
qu.1.8.fixed=@

qu.1.9.mode=Multiple Choice@
qu.1.9.name=09. Smoking & Pregnancy@
qu.1.9.comment=@
qu.1.9.editing=useHTML@
qu.1.9.solution=@
qu.1.9.algorithm=$Q=9;
$U1=range(0.2,0.25,0.001);
$N=range(200,250,1);
$U=100*$U1;
$n=range(30,35,1);
$P=$n/$N;
$S=sqrt($U1*(1-$U1)/$N);
$T=-($P-$U1)/$S;
$Z=maple("stats[statevalf,cdf,normald]($T)");
$PV=1-$Z;
$ANS=if(le($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT=if(ge($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.1.9.uid=d9273ffb-4730-4987-b8bc-9c46850898f7@
qu.1.9.info=  Course=202;
  Type=MC;
  Keyword=biology;
@
qu.1.9.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">A woman who smokes during pregnancy increases health risks to the infant. Suppose that a sample of $N pregnant women who smoked prior to prenancy contained $n who quit smoking during pregnancy.&nbsp; 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></mstyle></math>denote the true proportion of female smokers who quit smoking during pregnancy.<br />
<br />
H<sub>0</sub>: <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></mstyle></math>= $U1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></mstyle></math>< $U1
<p>Does this data support the theory that fewer than $U% of female smokers quit smoking during pregnancy? Assume normality (<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&alpha;</mi></mrow></mstyle></math> = 0.05).<span style="vertical-align: -5px"><br />
</span></p>
</div>@
qu.1.9.answer=1@
qu.1.9.choice.1=$ANS@
qu.1.9.choice.2=$ALT@
qu.1.9.fixed=@

qu.1.10.mode=Multiple Choice@
qu.1.10.name=06. Blood Pressure@
qu.1.10.comment=@
qu.1.10.editing=useHTML@
qu.1.10.solution=@
qu.1.10.algorithm=$Q=6;
$U=range(126,128,0.01);
$S=range(6,8,0.01);
$Xbar=range(128,129,0.01);
$N=range(50,60,1);
$T=($Xbar-$U)/($S/sqrt($N));
$Z=maple("stats[statevalf,cdf,normald]($T)");
$PV=2*(1-$Z);
$ANS=if(le($PV,0.01),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT=if(ge($PV,0.01),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.1.10.uid=23fd49a3-c630-44ce-ac61-925fca759832@
qu.1.10.info=  Course=202;
  Keyword=biology;
  Type=MC;
@
qu.1.10.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Normal Approximation/Q$Q">The mean systolic blood pressure for white males aged 35-44 in Canada is $U. A report said that the mean blood pressure and standard deviation of a sample of $N diabetic males aged 35-44 are $Xbar and $S, respectively. The researchers were interested in determining whether the mean systolic blood pressure of 35-44 year old diabetic males differed from that of 35-44 year-old males in the general population. Assume normality.(<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> = 0.01)&nbsp;
<p><br />
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></mstyle></math>denote the true mean systolic blood pressure for diabetic males aged 35-44</p>
<p>H<sub>0</sub>: <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></mstyle></math>= $U&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></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><mo lspace='0.0em' rspace='0.0em'>&ne;</mo></mrow></mstyle></math> $U&nbsp;</p>
<p>What should the researchers conclude?</p>
</div>@
qu.1.10.answer=1@
qu.1.10.choice.1=$ANS@
qu.1.10.choice.2=$ALT@
qu.1.10.fixed=@

qu.2.topic=Student t@

qu.2.1.mode=Multiple Choice@
qu.2.1.name=03. EPA@
qu.2.1.comment=@
qu.2.1.editing=useHTML@
qu.2.1.solution=@
qu.2.1.algorithm=$Q=3;
$U=range(13,15,0.01);
$S=range(6,8,0.01);
$Xbar=range(15,20,0.01);
$N=range(10,15);
$T=($Xbar-$U)/($S/sqrt($N));
$DF=$N-1;
$Z=maple("stats[statevalf,cdf,studentst[$DF]]($T)");
$PV=(1-$Z);
$ANS=if(le($PV,0.05),"Reject Null Hypothesis","Failed to Reject Null Hypothesis");
$ALT=if(ge($PV,0.05),"Reject Null Hypothesis","Failed to Reject Null Hypothesis");@
qu.2.1.uid=15e541e2-6ce1-479d-8d13-143c084fc335@
qu.2.1.info=  Course=202;
  Type=MC;
  Keyword=biology;
@
qu.2.1.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Student t/Q$Q">Federal officials have investigated the problems associated with disposal of hazardous wastes. One disposal site is the abandoned Stringfellow acid pits in Riverside County, Calif. The EPA sampled water from $N wells in nearby Glen Avon. The EPA standard for maximum allowable radiation level of drinking water is $U pCi/L. Suppose that the sample of $N water specimens resulted in a sample mean radiation level of $Xbar pCi/L and a sample standard deviation $S. Is this sufficient evidence to indicate that the water in Glen Avon has a mean radiation level that exceeds the EPA standard?&nbsp; Use t test. (<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> = 0.05)
<p>H<sub>0</sub>: <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></mstyle></math>= $U&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></mstyle></math>> $U</p>
<p>Let <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;</mi></mrow></mstyle></math>denote the true mean radiation level for well water in Glen Avon</p>
<p><span style="vertical-align: -5px;"><br />
</span></p>
</div>@
qu.2.1.answer=1@
qu.2.1.choice.1=$ANS@
qu.2.1.choice.2=$ALT@
qu.2.1.fixed=@

qu.2.2.mode=Multiple Choice@
qu.2.2.name=01. Amazon soil pH@
qu.2.2.comment=@
qu.2.2.editing=useHTML@
qu.2.2.solution=@
qu.2.2.algorithm=$Q=1;
$U=range(5,5.5,0.01);
$S=range(0.6,0.8,0.01);
$Xbar=range(5.5,6.0,0.01);
$N=range(20,25,1);
$T=($Xbar-$U)/($S/sqrt($N));
$DF=$N-1;
$Z=maple("stats[statevalf,cdf,studentst[$DF]]($T)");
$PV=2*(1-$Z);
$ANS=if(le($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT=if(ge($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.2.2.uid=e39a46d1-efb1-47e9-af03-ca55fef61e8c@
qu.2.2.info=  Type=MC;
  Course=202;
  Keyword=biology;
@
qu.2.2.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Student t/Q$Q">The low population density of the Amazon region has long puzzled geographers and other social scientists. Some have suggested that environment conditions are inimical or unfriendly, to support a large population. However, some scientists suggested otherwise. Their judgement rests largely on an analysis of $N black-earth soil samples, which gives evidence of the presence of large Indian populations prior to the European influx. Data of black-earth pH samples were collected and summarized, with sample mean of $Xbar and standard deviation of $S. Do these data indicate that the true average black-earth pH differs from $U, the pH value for many other types of soil in the region?&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>&alpha;</mi></mrow></mstyle></math> = 0.05). Use t-test.
<p>H<sub>0</sub>: <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></mstyle></math>= $U&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></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><mo lspace='0.0em' rspace='0.0em'>&ne;</mo></mrow></mstyle></math> $U</p>
<p>&nbsp;</p>
<p>Let <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;</mi></mrow></mstyle></math>denote the true average black-earth soil pH in Amazonia</p>
<p><span style="vertical-align: -5px;"><br />
</span></p>
</div>@
qu.2.2.answer=1@
qu.2.2.choice.1=$ANS@
qu.2.2.choice.2=$ALT@
qu.2.2.fixed=@

qu.2.3.mode=Multiple Choice@
qu.2.3.name=02. Childern Growth Rate@
qu.2.3.comment=@
qu.2.3.editing=useHTML@
qu.2.3.solution=@
qu.2.3.algorithm=$Q=2;
$U=range(130,135,0.01);
$S=range(6,8,0.01);
$Xbar=range(135,140,0.01);
$N=range(10,15);
$T=($Xbar-$U)/($S/sqrt($N));
$DF=$N-1;
$Z=maple("stats[statevalf,cdf,studentst[$DF]]($T)");
$PV=(1-$Z);
$ANS=if(le($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");
$ALT=if(ge($PV,0.05),"Reject Null Hypothesis","Fail to Reject Null Hypothesis");@
qu.2.3.uid=c660c909-2621-4a54-a243-270348d4b2c3@
qu.2.3.info=  Course=202;
  Type=MC;
  Keyword=biology;
@
qu.2.3.question=<div title="UW Statistics Bank/Hypothesis Testing/One Sample/Student t/Q$Q">Extensive data collected during the first half of this century showed clearly that in those years, American-born Japanese childern grew faster than did Japanese-born children. A research paper conjectured that improved economic and environmental conditions in postwar Japan had greatly narrowed this gap. To investigate the validity of this conjecture, a large sample of Hawaiian-born Japanese children was obtained, and the children were categorized with respect to age. There were $N 11-year-old boys in the sample. The sample average height of these $N boys was $Xbar cm and the sample standard deviation was $S cm. The average height of native-born-11-year-old Japanese children at that time was known to be $U cm. Does this data suggest that the true average height of Hawaiian born male exceeds their native-born counterpart? Use t test. (<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> = 0.05)
<p>H<sub>0</sub>: <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></mstyle></math>= $U&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; versus&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; H<sub>1</sub>: <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></mstyle></math>> $U</p>
<p>Let <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&mu;</mi></mrow></mstyle></math>denote the true average height for all Hawaiian-born 11-year-old male Japanese children.</p>
<p><span style="vertical-align: -5px"><br />
</span></p>
</div>@
qu.2.3.answer=1@
qu.2.3.choice.1=$ANS@
qu.2.3.choice.2=$ALT@
qu.2.3.fixed=@

