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<h2 class="hd hd-2 unit-title">NHST III</h2>
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<h2 class="hd hd-2 unit-title">Class 19 reading questions: NHST</h2>
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Problem 1
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Be sure to give your answers to at least 3 significant digits. The answer boxes also accept Matlab style arithmetic expressions. </p>
<p><b class="bf">1.</b> Suppose we have the following table of counts for the outcomes 0-6. </p>
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<td style="border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:left; border-left:1px solid black; border:none">
Outcome </td>
<td style="border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:left; border:none">
0 </td>
<td style="border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:left; border:none">
1 </td>
<td style="border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:left; border:none">
2 </td>
<td style="border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:left; border:none">
3 </td>
<td style="border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:left; border:none">
4 </td>
<td style="border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:left; border:none">
5 </td>
<td style="border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:left; border-right:1px solid black; border:none">
6</td>
</tr>
<tr>
<td style="text-align:left; border-left:1px solid black; border-bottom-style:solid; border-bottom-color:black; border-bottom-width:1px; border:none">
Observed </td>
<td style="text-align:left; border-bottom-style:solid; border-bottom-color:black; border-bottom-width:1px; border:none">
5 </td>
<td style="text-align:left; border-bottom-style:solid; border-bottom-color:black; border-bottom-width:1px; border:none">
11 </td>
<td style="text-align:left; border-bottom-style:solid; border-bottom-color:black; border-bottom-width:1px; border:none">
13 </td>
<td style="text-align:left; border-bottom-style:solid; border-bottom-color:black; border-bottom-width:1px; border:none">
7 </td>
<td style="text-align:left; border-bottom-style:solid; border-bottom-color:black; border-bottom-width:1px; border:none">
2 </td>
<td style="text-align:left; border-bottom-style:solid; border-bottom-color:black; border-bottom-width:1px; border:none">
1 </td>
<td style="text-align:left; border-right:1px solid black; border-bottom-style:solid; border-bottom-color:black; border-bottom-width:1px; border:none">
1</td>
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<p>
We suggest you use R to do the computations for this problem. Here is the data in a form you should be able to copy and paste into R studio.<br/><code> outcomes = 0:6 <br/> observed = c(5, 11, 13, 7, 2, 1, 1)</code> </p>
<p>
We hypothesize that the data is drawn from a binomial(6, 0.4) distribution. </p>
<p><b class="bf">(a)</b> Compute the likelihood ratio statistic. (Give 4 significant digits.) <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_c19-rq11_2_1" class=" capa_inputtype textline">
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<p><b class="bf">(b)</b> Compute the Pearson chi square statistic [mathjaxinline]X^2[/mathjaxinline]. (Give 4 significant digits) <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_c19-rq11_3_1" class=" capa_inputtype textline">
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<p><b class="bf">(c)</b> How many degrees of freedom are there in the chi square null distribution? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_c19-rq11_4_1" class=" capa_inputtype textline">
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<p><b class="bf">(d)</b> Compute the [mathjaxinline]p[/mathjaxinline]-value (based on the [mathjaxinline]G[/mathjaxinline] statistic). (Give 2 significant digits.) <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_c19-rq11_5_1" class=" capa_inputtype textline">
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