qu.1.topic=HT Hypothesis Testing Basics@

qu.1.1.mode=Multiple Choice@
qu.1.1.name=07. Sea Cucumbers@
qu.1.1.comment=@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$Q=7;
$N1=range(10,15,1);
$N2=range(1,10,1);
$ANS=$N1+$N2-2;
$ALT1=$N1+$N2-1;
$ALT2=$N1+$N2;
$ALT3=min($N1,$N2);@
qu.1.1.uid=65044522-d213-4135-9053-58c1201804b1@
qu.1.1.info=  Course=202;
  Course=232;
  Keyword=biology;
  Type=MC;
@
qu.1.1.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Basics/Q$Q">A study on the oxygen consumption rate (OCR) of sea cucumbers involved a random sample of size&nbsp;$N1 at 15<sup>o</sup>C and a second random sample of size&nbsp;$N2 kept at 18<sup>o</sup>C. If one tested the hypothesis that this range of temperature had no effect on the OCR, the liberal degrees of freedom for the test statistic would be</div>@
qu.1.1.answer=3@
qu.1.1.choice.1=$ALT1@
qu.1.1.choice.2=$ALT2@
qu.1.1.choice.3=$ANS@
qu.1.1.choice.4=$ALT3@
qu.1.1.fixed=@

qu.1.2.mode=Multiple Choice@
qu.1.2.name=08. Arm length@
qu.1.2.comment=<p>The attribute under study is the difference in arm length from a person's left to right arm.&nbsp; Since there is one observation of this per individual in the population, the degrees of freedom is $N1 - 1 = $ANS</p>@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$Q=8;
$N1=range(10,15,1);
$ANS=$N1-1;
$ALT1=$N1+1;
$ALT2=2*$N1-2;
$ALT3=2*$N1-1;@
qu.1.2.uid=5d53ce73-e739-4c17-b24d-4ce5f1cc7bae@
qu.1.2.info=  Course=202;
  Course=232;
  Keyword=biology;
  Type=MC;
@
qu.1.2.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Basics/Q$Q">A medical researcher is interested in whether patients' left arms or right arms are longer. If $N1 patients participate in this study (so that $N1 left arms and $N1 right arms are measured), how many degrees of freedom should the researcher use in her t-test critical value?</div>@
qu.1.2.answer=1@
qu.1.2.choice.1=$ANS@
qu.1.2.choice.2=$ALT1@
qu.1.2.choice.3=$ALT2@
qu.1.2.choice.4=$ALT3@
qu.1.2.fixed=@

qu.1.3.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Basics/Q14">The critical value for a left-tailed t-test for dependent samples when the degrees of freedom = 7 and &alpha; = 0.025 is :&nbsp;&nbsp; (4 decimals)</div>@
qu.1.3.answer.num=-2.365@
qu.1.3.answer.units=@
qu.1.3.showUnits=false@
qu.1.3.grading=toler_abs@
qu.1.3.err=0.001@
qu.1.3.negStyle=minus@
qu.1.3.numStyle=thousands scientific dollars arithmetic@
qu.1.3.mode=Numeric@
qu.1.3.name=14. Left-tailed t-test CP@
qu.1.3.comment=<p>Looking at a t-table, with the specified degrees of freedom and <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>, the value 2.365 shows up.&nbsp; Since the test is a one-sided left-tailed test, this limiting value should be negative because the tail is to the left of 0.</p>@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=@
qu.1.3.uid=8001ac22-25a3-435d-8d25-13f90096d783@
qu.1.3.info=  Type=numeric;
  Course=202;
  Algorithmic=no;
@

qu.1.4.mode=Multiple Choice@
qu.1.4.name=13. Type I error for Egg Size@
qu.1.4.comment=<p>Type I error occurs when a true null hypothesis is rejected in favour of the alternate hypothesis.&nbsp; In this case, Type I error means that we reject the hypothesis that larger nests have the same size of eggs as smaller nests.</p>@
qu.1.4.editing=useHTML@
qu.1.4.solution=@
qu.1.4.algorithm=@
qu.1.4.uid=10c05e9d-5267-4eed-a38c-80af9c501f60@
qu.1.4.info=  Type=MC;
  Course=202;
  Algorithmic=no;
@
qu.1.4.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Basics/Q13">A researcher wants to see if birds that build larger nests lay larger eggs. She selects two random samples of nests: one of small nests and the other of large nests. She measures one egg from each nest. The data are summarized below.
<p>&nbsp;</p>
<p><img height="535" width="569" title="Egg size data [IMG:Eggsize.gif]" src="__BASE_URI__HT/Basics/Eggsize.gif" alt="Egg size data" /></p>
<p>A Type I (false positive) error would occur if:</p>
</div>@
qu.1.4.answer=4@
qu.1.4.choice.1=We conclude that larger nests have the same size eggs (on average) when in fact they are larger.@
qu.1.4.choice.2=We conclude that larger nests have larger eggs (on average) when in fact they are larger.@
qu.1.4.choice.3=We conclude that larger nests have the same size eggs (on average) when in fact there is no difference in the mean.@
qu.1.4.choice.4=We conclude that larger nests had larger eggs (on average) when in fact there is no difference in the mean.@
qu.1.4.choice.5=I ever take a statistics course again in my life! (just kidding).@
qu.1.4.fixed=@

qu.1.5.mode=Multiple Choice@
qu.1.5.name=11. t-test dependent@
qu.1.5.comment=@
qu.1.5.editing=useHTML@
qu.1.5.solution=@
qu.1.5.algorithm=@
qu.1.5.uid=87558ae3-c6e4-4833-beff-de38647ced97@
qu.1.5.info=  Type=MC;
  Algorithmic=no;
  Course=202;
@
qu.1.5.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Basics/Q11">
<p>The formula of the t -test for dependent samples is:</p>
<p>&nbsp;</p>
</div>@
qu.1.5.answer=1@
qu.1.5.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><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mi>t</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mover><mrow><mi mathvariant='normal'>D</mi></mrow><mi>_</mi></mover><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msub><mi>&mu;</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub></mrow></mrow><mrow><msub><mi>s</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub><mo lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&sol;</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.1.5.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><mi>t</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mover><mrow><mi mathvariant='normal'>D</mi></mrow><mi>&macr;</mi></mover><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msub><mi>&mu;</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub></mrow></mrow><mrow><msub><mi>s</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.1.5.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><mi>t</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mover><mrow><mi mathvariant='normal'>D</mi></mrow><mi>&macr;</mi></mover><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msub><mi>&mu;</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub></mrow></mrow><mrow><msub><mi>s</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub><mo lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&sol;</mo><mrow><mi>n</mi></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.1.5.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><mi>t</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msub><mi>&mu;</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mover><mrow><mi mathvariant='normal'>D</mi></mrow><mi>&#x005e;</mi></mover></mrow><mrow><msub><mi>s</mi><mrow><mi mathvariant='normal'>D</mi></mrow></msub><mo lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&sol;</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.1.5.fixed=@

qu.1.6.mode=Multiple Choice@
qu.1.6.name=09. Feed and Weight Gain@
qu.1.6.comment=<p>The two-sample t-test tests the null hypothesis that the mean of two  populations is the same.&nbsp; In this case the two populations are the  animals while eating the old feed, and the animals while eating  the new feed.&nbsp; The p-value is the probability of a more rare (more difference in weight gained) occurrence, given that the  null hypothesis is true.</p>@
qu.1.6.editing=useHTML@
qu.1.6.solution=@
qu.1.6.algorithm=$Q="09";
$P=range(0.001,0.09,0.001);
$PER=100*$P;
$Gain=range(8,15);@
qu.1.6.uid=5b3076a7-6f6d-4823-9695-f8d1aeb9c10c@
qu.1.6.info=  Type=MC;
  Course=202;
@
qu.1.6.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Basics/Q$Q">We wish to test if a new feed increases the mean weight gain compared to an old feed. At the conclusion of the experiment it was found that the new feed gave a $Gain kg bigger gain than the old feed. A two-sample t-test with the proper one-sided alternative was done and the resulting p-value was $P. This means:</div>@
qu.1.6.answer=2@
qu.1.6.choice.1=There is an $PER% chance the null hypothesis is true.@
qu.1.6.choice.2=There was only a $PER% chance of observing an increase greater than $Gain kg (assuming the null hypothesis was true).@
qu.1.6.choice.3=There was only an $PER% chance of observing an increase greater than $Gain kg (assuming the null hypothesis was false).@
qu.1.6.choice.4=There is an $PER% chance the alternate hypothesis is true.@
qu.1.6.choice.5=There is only an $PER% chance of getting a $Gain kg increase.@
qu.1.6.fixed=@

qu.1.7.mode=Multiple Choice@
qu.1.7.name=05. Power of test@
qu.1.7.comment=<p>Type II error is when a false null hypothesis is not rejected.&nbsp; <mi><mi><mi>&beta;</mi></mi></mi> is the probability of failing to reject null hypothesis H<sub>0</sub> given that H<sub>A </sub>is true.&nbsp; 1-<mi></mi>&beta; is the opposite of this, so the probability of rejecting H<sub>0</sub> given H<sub>A</sub> is true.</p>@
qu.1.7.editing=useHTML@
qu.1.7.solution=@
qu.1.7.algorithm=@
qu.1.7.uid=f4f1ab3b-9b12-433b-be2c-3089dee2b3e5@
qu.1.7.info=  Course=202;
  Type=MC;
@
qu.1.7.question=<div title="UW Statistics Bank/Hypothesis Testing/Basics/Q5">In hypothesis testing, &beta; is the probability of committing an error of Type II. The power of the test, 1 &minus; &beta; is then:</div>@
qu.1.7.answer=1@
qu.1.7.choice.1=the probability of rejecting H<sub>0</sub> when H<sub>A</sub> is true@
qu.1.7.choice.2=the probability of failing to reject H<sub>0</sub> when H<sub>A</sub> is true@
qu.1.7.choice.3=the probability of failing to reject H<sub>0</sub> when H<sub>0</sub> is true@
qu.1.7.choice.4=the probability of rejecting H<sub>0</sub> when H<sub>0</sub> is true@
qu.1.7.choice.5=the probability of failing to reject H<sub>0</sub>.@
qu.1.7.fixed=@

qu.1.8.mode=Multiple Choice@
qu.1.8.name=03. Polygraph Type II Error@
qu.1.8.comment=<p>Type II error is when a false null hypothesis is not rejected, also known as a "false negative".&nbsp; Given the null hypothesis that the suspect is innocent, we wish to test the probability that the Examiner judges a guilty suspect to be innocent.&nbsp; Based on the given numbers, this is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='10' 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'>guilty</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>parties</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>deemed</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>innocent</mi></mrow><mrow><mi mathvariant='normal'>guilty</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>parties</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>deemed</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>innocent</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>guilty</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>parties</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>deemed</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>guilty</mi></mrow></mfrac></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><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>$X2</mi><mrow><mi>$X2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>$X4</mi></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$ANS</mi></mrow></mstyle></math>.</p>@
qu.1.8.editing=useHTML@
qu.1.8.solution=@
qu.1.8.algorithm=$Q=3;
$X=200;
$X1=range(10,20,1);
$X2=range(20,30,1);
$X3=$X/2-$X1;
$X4=$X/2-$X2;
$ANS=$X2/($X2+$X4);
$ALT1=$X1/($X1+$X3);
$ALT2=$X2/$X;
$ALT3=$X1/$X;@
qu.1.8.uid=b20cd19d-cb48-4ed2-a699-5216d067d436@
qu.1.8.info=  Course=202;
  Type=MC;
@
qu.1.8.question=<div title="UW Statistics Bank/Hypothesis Testing/Basics/Q$Q">To determine the reliability of experts used in interpreting the results of polygraph examinations in criminal investigations,&nbsp;$X cases were studied. The results were:<br />
<table cellspacing="0" cellpadding="4" bordercolor="#111111" border="1" style="border-collapse: collapse;" id="AutoNumber1">
    <tbody>
        <tr>
            <td rowspan="2" colspan="2">&nbsp;</td>
            <td colspan="2">True Status</td>
        </tr>
        <tr>
            <td>Innocent</td>
            <td>Guilty</td>
        </tr>
        <tr>
            <td rowspan="2">Examiner's<br />
            Decision</td>
            <td>Innocent</td>
            <td align="center">$X1</td>
            <td align="center">$X2</td>
        </tr>
        <tr>
            <td>Guilty</td>
            <td align="center">$X3</td>
            <td align="center">$X4</td>
        </tr>
    </tbody>
</table>
If the hypotheses were H: suspect is innocent vs A: suspect is guilty, then we could estimate the probability of making a type II error as:</div>@
qu.1.8.answer=3@
qu.1.8.choice.1=$ALT1@
qu.1.8.choice.2=$ALT2@
qu.1.8.choice.3=$ANS@
qu.1.8.choice.4=$ALT3@
qu.1.8.fixed=@

qu.1.9.mode=Multiple Choice@
qu.1.9.name=01. Drug/diet/treatment Test@
qu.1.9.comment=<p>Her hypotheses are:</p>
<p>Ho:&nbsp; New $Test worse or equal to old<br />
Ha:&nbsp; New $Test better than old</p>
<p>For a type I error, she needs to reject the null hypothesis when it is actually true. So the answer is:</p>
<p><span>"she concludes that the new $Test is better when in fact the $Test\\s are equal in effectiveness."</span></p>@
qu.1.9.editing=useHTML@
qu.1.9.solution=@
qu.1.9.algorithm=$Q=1;
$Which=rint(3);
$Test=switch($Which,"drug","diet","treatment");
$Align=switch(rint(2),"Left","Right");@
qu.1.9.uid=a4bcf352-6397-4664-823f-351060208f02@
qu.1.9.info=  Keyword=biology;
  Course=232;
  Type=MC;
@
qu.1.9.question=<div title="UW Statistics Bank/Hypothesis Testing/Basics/Q$Q"><img hspace="4" align="$Align" alt="$Test" title="$Test [IMG:DrugDietTreatment$Which.gif]" src="__BASE_URI__HT/Basics/DrugDietTreat$Which.gif" />A researcher is going to conduct an experiment in order to compare two $Test\\s &ndash; a new $Test and an old $Test. The researcher would like to see whether there is sufficient evidence to say that the new $Test is better than the old $Test. In this problem, the researcher will commit a type I error if:</div>@
qu.1.9.answer=4@
qu.1.9.choice.1=she concludes that the $Test\\s are equal in effectiveness when in fact the new $Test is better.@
qu.1.9.choice.2=she concludes that the $Test\\s are equal in effectiveness when in fact the old $Test is better.@
qu.1.9.choice.3=she concludes that the old $Test is better when in fact the new $Test is better.@
qu.1.9.choice.4=she concludes that the new $Test is better when in fact the $Test\\s are equal in effectiveness.@
qu.1.9.choice.5=she concludes that the old $Test is better when in fact the $Test\\s are equal in effectiveness.@
qu.1.9.fixed=@

qu.1.10.mode=Multiple Choice@
qu.1.10.name=02. Feed and Weight Gain@
qu.1.10.comment=<p>The two-sample t-test tests the null hypothesis that the mean of two populations is the same. In this case the two populations are the animals (units) while eating the old feed, and the animals while eating the new feed. The p-value is the probability of a more rare (more different mean weight, so more weight gained) occurrence, given that the null hypothesis is true.&nbsp;</p>@
qu.1.10.editing=useHTML@
qu.1.10.solution=@
qu.1.10.algorithm=$Q=2;
$p=range(0.040,0.095,0.001);
$P=100*$p;
$Gain=range(4.5,11.5,0.1);@
qu.1.10.uid=355acb3e-914b-41d7-8619-764b59081dff@
qu.1.10.info=  Type=MC;
  Course=202;
@
qu.1.10.question=<div title="UW Statistics Bank/Hypothesis Testing/Basics/Q2">We wish to test if a new feed increases the mean weight gain compared to an old feed. At the conclusion of the experiment it was found that the new feed gave a $Gain kg bigger gain than the old feed. A two-sample t-test with the proper one-sided alternative was done and the resulting p-value was $p. This means:</div>@
qu.1.10.answer=2@
qu.1.10.choice.1=there is an $P% chance the null hypothesis is true.@
qu.1.10.choice.2=There was only a $P% chance of observing an increase greater than $Gain kg (assuming the null hypothesis was true).@
qu.1.10.choice.3=There was only an $P% chance of observing an increase greater than $Gain kg (assuming the null hypothesis was false).@
qu.1.10.choice.4=There is an $P% chance the alternate hypothesis is true.@
qu.1.10.choice.5=There is only an $P% chance of getting a $Gain kg increase.@
qu.1.10.fixed=@

qu.1.11.mode=Multiple Choice@
qu.1.11.name=11. Drug Test@
qu.1.11.comment=@
qu.1.11.editing=useHTML@
qu.1.11.solution=@
qu.1.11.algorithm=@
qu.1.11.uid=81f1e87a-5fed-468a-a6fe-edd45b3a14f3@
qu.1.11.info=  Type=MC;
  Course=202;
  Algorithmic=no;
@
qu.1.11.question=<div title="UW Statistics Bank/Hypothesis Testing/Basics/Q11">A researcher is going to conduct an experiment in order to compare two drugs &ndash; a new drug and an old drug. The researcher would like to see whether there is sufficient evidence to say that the new drug is better than the old drug. In this problem, the researcher will commit a type I error if:</div>@
qu.1.11.answer=4@
qu.1.11.choice.1=she concludes that the drugs are equal in effectiveness when in fact the new drug is better.@
qu.1.11.choice.2=she concludes that the drugs are equal in effectiveness when in fact the old drug is better.@
qu.1.11.choice.3=she concludes that the old drug is better when in fact the new drug is better.@
qu.1.11.choice.4=she concludes that the new drug is better when in fact the drugs are equal in effectiveness.@
qu.1.11.choice.5=she concludes that the old drug is better when in fact the drugs are equal in effectiveness.@
qu.1.11.fixed=@

qu.1.12.mode=Multiple Choice@
qu.1.12.name=10. DDT Poisoning@
qu.1.12.comment=<p>The confidence interval shows the range that 95% of data should fall into given previous information.&nbsp; Since this range does not include 0, at least 95% of the time the poisoned rats will not have the same mean numbers of tremors as the control rats.</p>@
qu.1.12.editing=useHTML@
qu.1.12.solution=@
qu.1.12.algorithm=@
qu.1.12.uid=4f969b62-7392-4bb7-9884-4f0029109604@
qu.1.12.info=  Type=MC;
  Course=202;
  Algorithmic=no;
@
qu.1.12.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Basics/Q10">In order to study the harmful effects of DDT poisoning, the pesticide was fed to 6 randomly chosen rats out of a group of 12 rats. The other 6 rats were used as the control group. The following data gives the measurements of the amount of tremor detected in the bodies of each rat after the experiment: The more tremor, the more harmful.&nbsp;
<p>&nbsp;</p>
<table cellspacing="1" cellpadding="3" border="0" id="AutoNumber1">
    <tbody>
        <tr>
            <td>Rat:</td>
            <td align="center">1</td>
            <td align="center">2</td>
            <td align="center">3</td>
            <td align="center">4</td>
            <td align="center">5</td>
            <td align="center">6</td>
        </tr>
        <tr>
            <td>Poisoned Group:</td>
            <td align="center">12.2</td>
            <td align="center">16.9</td>
            <td align="center">25.0</td>
            <td align="center">22.4</td>
            <td align="center">8.5</td>
            <td align="center">20.6</td>
        </tr>
        <tr>
            <td>Control Group:</td>
            <td align="center">11.1</td>
            <td align="center">12.1</td>
            <td align="center">9.3</td>
            <td align="center">6.6</td>
            <td align="center">9.6</td>
            <td align="center">8.2</td>
        </tr>
    </tbody>
</table>
<p>&nbsp;</p>
<p>A computer analysis is done with the output below (the differences are computed as control - poisoned)</p>
<table cellspacing="1" cellpadding="4" border="0" id="AutoNumber1">
    <tbody>
        <tr>
            <td><strong>t-test</strong></td>
            <td align="center">Difference</td>
            <td align="center">t-test</td>
            <td align="center">DF</td>
            <td align="center">Prob>|t|</td>
        </tr>
        <tr>
            <td>Estimate</td>
            <td align="center">-8.1167</td>
            <td align="center">-3.006</td>
            <td align="center">10</td>
            <td align="center">0.0132</td>
        </tr>
        <tr>
            <td>Std Error</td>
            <td align="center">2.7002</td>
            <td align="center">&nbsp;</td>
            <td align="center">&nbsp;</td>
            <td align="center">&nbsp;</td>
        </tr>
        <tr>
            <td>Lower 95%</td>
            <td align="center">-14.1331</td>
            <td align="center">&nbsp;</td>
            <td align="center">&nbsp;</td>
            <td align="center">&nbsp;</td>
        </tr>
        <tr>
            <td>Upper 95%</td>
            <td align="center">-2.1003</td>
            <td align="center">&nbsp;</td>
            <td align="center">&nbsp;</td>
            <td align="center">&nbsp;</td>
        </tr>
        <tr>
            <td colspan="5">
            <p align="center">(Assuming equal variances.)</p>
            </td>
        </tr>
    </tbody>
</table>
<p>Which of the following is correct?</p>
</div>@
qu.1.12.answer=4@
qu.1.12.choice.1=The p-value is small. There is good evidence that the two means are equal.@
qu.1.12.choice.2=The p-value is large. There is good evidence that the two means are different.@
qu.1.12.choice.3=The p-value is small. There is good evidence that the two sample means differ, in fact, the control group appears to have fewer tremors, on average. @
qu.1.12.choice.4=The confidence interval does not include 0. Hence, there is evidence that the mean number of tremors for all potential rats in the poisoned group is larger than that in the control group.@
qu.1.12.choice.5=The confidence interval does not include 0. Hence there is no evidence that the means are the same for both groups.@
qu.1.12.fixed=@

qu.1.13.mode=Multiple Choice@
qu.1.13.name=12. Hypotheses for egg size@
qu.1.13.comment=<p>The researcher is interested in determining whether larger birds lay larger eggs.&nbsp; This statement describes the alternate hypothesis that the mean egg size in larger nests is larger than the mean egg size in smaller nests, or <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>&mu;</mi><mrow><mi>L</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&gt;</mo><mrow><msub><mi>&mu;</mi><mrow><mi>S</mi></mrow></msub></mrow></mrow></mstyle></math>.&nbsp; The null hypothesis is that the egg size is the same no matter which nest the egg came from from, <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>&mu;</mi><mrow><mi>L</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msub><mi>&mu;</mi><mrow><mi>S</mi></mrow></msub></mrow></mrow></mstyle></math>.</p>@
qu.1.13.editing=useHTML@
qu.1.13.solution=@
qu.1.13.algorithm=@
qu.1.13.uid=fc155a77-0402-4be8-8afd-fa5541b673e0@
qu.1.13.info=  Type=MC;
  Algorithmic=no;
  Course=202;
@
qu.1.13.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Basics/Q12">A researcher wants to see if birds that build larger nests lay larger eggs. She selects two random samples of nests: one of small nests and the other of large nests. She measures one egg from each nest. The data are summarized below.
<p>&nbsp;</p>
<p><img height="535" width="569" alt="Egg size data" src="__BASE_URI__HT/Basics/Eggsize.gif" title="Egg size data [IMG:Eggsize.gif]" /></p>
<p>The null and alternate hypothesis of interest is:</p>
</div>@
qu.1.13.answer=1@
qu.1.13.choice.1=H : &mu;<sub>L</sub> = &mu;<sub>S</sub>; A : &mu;<sub>L</sub> &gt; &mu;<sub>S</sub>@
qu.1.13.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><mi>H</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><mover><mrow><msub><mi>Y</mi><mrow><mi>L</mi></mrow></msub></mrow><mi>&macr;</mi></mover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mover><mrow><msub><mi>Y</mi><mrow><mi>S</mi></mrow></msub></mrow><mi>&macr;</mi></mover><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo separator='true' lspace='0.0em' rspace='0.2777778em'>&semi;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mover><mrow><msub><mi>Y</mi><mrow><mi>L</mi></mrow></msub></mrow><mi>&macr;</mi></mover><mo lspace='0.2777778em' rspace='0.2777778em'>&gt;</mo><mrow><mover><mrow><msub><mi>Y</mi><mrow><mi>S</mi></mrow></msub></mrow><mi>&macr;</mi></mover></mrow></mrow></mstyle></math>@
qu.1.13.choice.3=H : &mu;<sub>L</sub> = &mu;<sub>S</sub>;&nbsp;&nbsp; A : &mu;L&ne; &mu;<sub>S</sub>@
qu.1.13.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><mi>H</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><mover><mrow><msub><mi>Y</mi><mrow><mi>L</mi></mrow></msub></mrow><mi>&macr;</mi></mover><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mover><mrow><msub><mi>Y</mi><mrow><mi>S</mi></mrow></msub></mrow><mi>&macr;</mi></mover><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo separator='true' lspace='0.0em' rspace='0.2777778em'>&semi;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>A</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&colon;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mover><mrow><msub><mi>Y</mi><mrow><mi>L</mi></mrow></msub></mrow><mi>&macr;</mi></mover><mo lspace='0.2777778em' rspace='0.2777778em'>&ne;</mo><mover><mrow><msub><mi>Y</mi><mrow><mi>S</mi></mrow></msub></mrow><mi>&macr;</mi></mover></mrow></mstyle></math>@
qu.1.13.choice.5=H : &mu;<sub>L</sub> = &mu;<sub>S</sub>; A : &mu;<sub>L</sub> &lt; &mu;<sub>S</sub>@
qu.1.13.fixed=@

qu.1.14.mode=Multiple Choice@
qu.1.14.name=9. Power of 1 - &#946;@
qu.1.14.comment=@
qu.1.14.editing=useHTML@
qu.1.14.solution=@
qu.1.14.algorithm=$Q=9;@
qu.1.14.uid=106e33f9-17ef-469b-b57c-3a5f27023ce5@
qu.1.14.question=<div title="STAT202/Test 8/Hypothesis Testing/Q$Q [3-2]">In hypothesis testing, &beta;  is the probability of committing an error of Type II. The power of the test, 1 &minus;  &beta; is then:</div>@
qu.1.14.answer=1@
qu.1.14.choice.1=the probability of rejecting H<sub>0</sub> when H<sub>A</sub> is true@
qu.1.14.choice.2=the probability of failing to reject H<sub>0</sub> when H<sub>A</sub> is true@
qu.1.14.choice.3=the probability of failing to reject H<sub>0</sub> when H<sub>0</sub> is true@
qu.1.14.choice.4=the probability of rejecting H<sub>0</sub> when H<sub>0</sub> is true@
qu.1.14.choice.5=the probability of failing to reject H<sub>0</sub>.@
qu.1.14.fixed=@

qu.1.15.mode=Multiple Choice@
qu.1.15.name=04. Polygraph Type I error@
qu.1.15.comment=<p>Type I error is when a true null hypothesis is rejected.&nbsp; In this case, this is the probability of the Examiner judging an innocent suspect to be guilty.&nbsp; The probability 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><mfrac><mrow><mi>innocent</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>parties</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>deemed</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>guilty</mi></mrow><mrow><mi>innocent</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>parties</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>deemed</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>guilty</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>innocent</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>parties</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>deemed</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>innocent</mi></mrow></mfrac></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='0.2777778em' 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>$X3</mi><mrow><mi>$X1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>$X3</mi></mrow></mfrac></mrow><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$ANS</mi></mrow></mstyle></math></p>@
qu.1.15.editing=useHTML@
qu.1.15.solution=@
qu.1.15.algorithm=$Q=4;
$X=300;
$X1=range(10,20,1);
$X2=range(20,30,1);
$X3=$X/2-$X1;
$X4=$X/2-$X2;
$ANS=decimal(3,$X3/($X1+$X3));
$ALT1=decimal(3,$X1/($X1+$X3));
$ALT2=decimal(3,$X2/($X2+$X4));
$ALT3=decimal(3,$X1/$X);@
qu.1.15.uid=30b83008-0b16-4034-9e40-394e8340793c@
qu.1.15.info=  Course=202;
  Type=MC;
@
qu.1.15.question=<div title="UW Statistics Bank/Hypothesis Testing/Basics/Q$Q">To determine the reliability of experts used in interpreting the results of polygraph examinations in criminal investigations,&nbsp;$X cases were studied. The results were:<br />
<table cellspacing="0" cellpadding="4" bordercolor="#111111" border="1" style="border-collapse: collapse;" id="AutoNumber1">
    <tbody>
        <tr>
            <td rowspan="2" colspan="2">&nbsp;</td>
            <td colspan="2">True Status</td>
        </tr>
        <tr>
            <td>Innocent</td>
            <td>Guilty</td>
        </tr>
        <tr>
            <td rowspan="2">Examiner's<br />
            Decision</td>
            <td>Innocent</td>
            <td align="center">$X1</td>
            <td align="center">$X2</td>
        </tr>
        <tr>
            <td>Guilty</td>
            <td align="center">$X3</td>
            <td align="center">$X4</td>
        </tr>
    </tbody>
</table>
If the hypotheses were H: suspect is innocent vs A: suspect is guilty, then we could estimate the probability of making a type&nbsp;I error as:</div>@
qu.1.15.answer=3@
qu.1.15.choice.1=$ALT1@
qu.1.15.choice.2=$ALT2@
qu.1.15.choice.3=$ANS@
qu.1.15.choice.4=$ALT3@
qu.1.15.fixed=@

qu.1.16.mode=Multiple Choice@
qu.1.16.name=10. Preflight check@
qu.1.16.comment=@
qu.1.16.editing=useHTML@
qu.1.16.solution=@
qu.1.16.algorithm=@
qu.1.16.uid=d269b854-ca88-4be1-bc2f-2ba42d710a61@
qu.1.16.info=  Type=MC;
  Course=202;
@
qu.1.16.question=<div title="UW Statistics Bank/Hypothesis Testing/Basics/Q10">During the pre-flight check, Pilot Jones discovers a minor problem - a warning light indicates that the fuel guage may be broken. If Jones decides to check the fuel level by hand, it will delay the flight by 45 minutes. If Jones decides to ignore the warning, the aircraft may run out of fuel before it gets to Gimli. In this situation, what would be:<br />
<br />
i) the appropriate null hypothesis? and;<br />
ii) a type I error?</div>@
qu.1.16.answer=1@
qu.1.16.choice.1=Null Hypothesis: assume that the warning can be ignored. Type I error: decide to check the fuel by hand when there is in fact enough fuel.@
qu.1.16.choice.2=Null Hypothesis: assume that the warning can be ignored. Type I error: decide to ignore the warning when there is in fact not enough fuel.@
qu.1.16.choice.3=Null Hypothesis: assume that the fuel should be checked by hand. Type I error: decide to ignore the warning when there is in fact not enough fuel.@
qu.1.16.choice.4=Null Hypothesis: assume that the fuel should be checked by hand. Type I error: decide to check the fueld by hand when there is in fact enough fuel.@
qu.1.16.choice.5=Null Hypothesis: assume that the aircraft is already late. Type I error: taking a commercial flight to Gimli in the first place.@
qu.1.16.fixed=@

qu.1.17.mode=Multiple Choice@
qu.1.17.name=06. Preflight check@
qu.1.17.comment=@
qu.1.17.editing=useHTML@
qu.1.17.solution=@
qu.1.17.algorithm=$Q=6;
$Pilot=switch(rint(4),"Jones","Smith","VanDerBoek","Singh");
$Delay=range(30,55,5);
$Which=rint(5);
$Align=switch(rint(2),"Left","Right");@
qu.1.17.uid=c7968f8a-daba-497a-8853-d082e5145bd8@
qu.1.17.info=  Course=202;
  Type=MC;
@
qu.1.17.question=<div title="University of Waterloo Statistics Bank/Hypothesis Testing/Basics/Q$Q">
<img hspace="4" align="$Align" src="__BASE_URI__HT/Basics/Plane$Which.gif" alt="Airplane" title="Airplane [IMG:Plane$Which.gif]" />During the pre-flight check, Pilot $Pilot discovers a minor problem - a warning light indicates that the fuel guage may be broken. If $Pilot decides to check the fuel level by hand, it will delay the flight by $Delay minutes. If $Pilot decides to ignore the warning, the aircraft may run out of fuel before it gets to Gimli. In this situation, what would be:
<p>&nbsp;</p><p>&nbsp;</p>
i) the appropriate null hypothesis? and;<br />
ii) a type I error?</p>
</div>@
qu.1.17.answer=1@
qu.1.17.choice.1=Null Hypothesis: assume that the warning can be ignored. Type I error: decide to check the fuel by hand when there is in fact enough fuel.@
qu.1.17.choice.2=Null Hypothesis: assume that the warning can be ignored. Type I error: decide to ignore the warning when there is in fact not enough fuel.@
qu.1.17.choice.3=Null Hypothesis: assume that the fuel should be checked by hand. Type I error: decide to ignore the warning when there is in fact not enough fuel.@
qu.1.17.choice.4=Null Hypothesis: assume that the fuel should be checked by hand. Type I error: decide to check the fueld by hand when there is in fact enough fuel.@
qu.1.17.choice.5=Null Hypothesis: assume that the aircraft is already late. Type I error: taking a commercial flight to Gimli in the first place.@
qu.1.17.fixed=@

