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@@ -62,7 +62,7 @@ window.MathJax = {
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@@ -79,7 +79,7 @@ window.MathJax = {
<meta property="og:type" content="book">
<meta property="book:title" content="Math 1044 Notes">
<meta property="book:author" content="Andy Eisenberg">
<script src="_static/pretext/js/lib/jquery.min.js"></script><script src="_static/pretext/js/lib/jquery.sticky.js"></script><script src="_static/pretext/js/lib/jquery.espy.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><script src="_static/pretext/js/user_preferences.js"></script><!--** eBookCongig is necessary to configure interactive **-->
<script src="_static/pretext/js/jquery.min.js"></script><script src="_static/pretext/js/pretext.js"></script><script src="_static/pretext/js/pretext_add_on.js?x=1"></script><!--** eBookCongig is necessary to configure interactive **-->
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<body class="pretext book ignore-math">
@@ -151,6 +151,9 @@ eBookConfig.enable_chatcodes = false;
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@@ -244,12 +247,16 @@ eBookConfig.enable_chatcodes = false;
<div class="toc-title-box"><a href="ch-Confidence-Intervals.html" class="internal"><span class="codenumber">4</span> <span class="title">Confidence Intervals</span></a></div>
<ul class="structural toc-item-list contains-active">
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Central Limit Theorem</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
<div class="toc-title-box"><a href="sec-Likelihood.html" class="internal"><span class="codenumber">4.1</span> <span class="title">Likelihood</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Likelihood.html#sec-Likelihood-20" class="internal"><span class="codenumber">4.1</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
<li class="toc-item toc-section">
<div class="toc-title-box"><a href="sec-CLT.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Central Limit Theorem</span></a></div>
<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-CLT.html#exercises-CLT" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
<li class="toc-item toc-section contains-active">
<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.2</span> <span class="title">Confidence Intervals</span></a></div>
<ul class="structural toc-item-list active"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.2</span> <span class="title">Exercises</span></a></div></li></ul>
<div class="toc-title-box"><a href="sec-Confidence-Intervals.html" class="internal"><span class="codenumber">4.3</span> <span class="title">Confidence Intervals</span></a></div>
<ul class="structural toc-item-list active"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Confidence-Intervals.html#exercises-Confidence-Intervals" class="internal"><span class="codenumber">4.3</span> <span class="title">Exercises</span></a></div></li></ul>
</li>
</ul>
</li>
@@ -290,7 +297,7 @@ eBookConfig.enable_chatcodes = false;
<li class="toc-item toc-backmatter"><div class="toc-title-box"><a href="backmatter.html" class="internal"><span class="title">Backmatter</span></a></div></li>
</ul></nav></div>
<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-Confidence-Intervals"><h2 class="heading hide-type">
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Confidence Intervals</span>
<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.3</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Confidence Intervals</span>
</h2>
<div class="para" id="sec-Confidence-Intervals-2">Text of section.<div class="autopermalink" data-description="Paragraph"><a href="#sec-Confidence-Intervals-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div>
@@ -300,18 +307,18 @@ eBookConfig.enable_chatcodes = false;
<article class="exercise exercise-like" id="exercises-Confidence-Intervals-1"><h4 class="heading"><span class="codenumber">1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
<div class="para" id="exercises-Confidence-Intervals-1-1-1">Suppose we flip a coin 100 times and count 60 heads. Let <span class="process-math">\(p\)</span> be the (unknown) probability that the coin comes up heads on a flip. Give an approximate 95% confidence interval for the value of <span class="process-math">\(p\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div>
<div class="autopermalink" data-description="Exercise 4.2.1"><a href="#exercises-Confidence-Intervals-1" title="Copy heading and permalink for Exercise 4.2.1" aria-label="Copy heading and permalink for Exercise 4.2.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
<div class="autopermalink" data-description="Exercise 4.3.1"><a href="#exercises-Confidence-Intervals-1" title="Copy heading and permalink for Exercise 4.3.1" aria-label="Copy heading and permalink for Exercise 4.3.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
<div class="introduction" id="exercises-Confidence-Intervals-2-1"><div class="para" id="exercises-Confidence-Intervals-2-1-1">Suppose in a sample of 100 people, 12 are left-handed.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div></div>
<article class="task exercise-like" id="exercises-Confidence-Intervals-2-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
<div class="para" id="exercises-Confidence-Intervals-2-2-1-1">Give a 95% confidence interval for the proportion <span class="process-math">\(p\)</span> of left-handed people.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-2-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div>
<div class="autopermalink" data-description="Task 4.2.2.a"><a href="#exercises-Confidence-Intervals-2-2" title="Copy heading and permalink for Task 4.2.2.a" aria-label="Copy heading and permalink for Task 4.2.2.a">🔗</a></div></article><article class="task exercise-like" id="exercises-Confidence-Intervals-2-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
<div class="autopermalink" data-description="Task 4.3.2.a"><a href="#exercises-Confidence-Intervals-2-2" title="Copy heading and permalink for Task 4.3.2.a" aria-label="Copy heading and permalink for Task 4.3.2.a">🔗</a></div></article><article class="task exercise-like" id="exercises-Confidence-Intervals-2-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
<div class="para" id="exercises-Confidence-Intervals-2-3-1-1">Give a 90% confidence interval.<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-2-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div>
<div class="autopermalink" data-description="Task 4.2.2.b"><a href="#exercises-Confidence-Intervals-2-3" title="Copy heading and permalink for Task 4.2.2.b" aria-label="Copy heading and permalink for Task 4.2.2.b">🔗</a></div></article><div class="autopermalink" data-description="Exercise 4.2.2"><a href="#exercises-Confidence-Intervals-2" title="Copy heading and permalink for Exercise 4.2.2" aria-label="Copy heading and permalink for Exercise 4.2.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
<div class="autopermalink" data-description="Task 4.3.2.b"><a href="#exercises-Confidence-Intervals-2-3" title="Copy heading and permalink for Task 4.3.2.b" aria-label="Copy heading and permalink for Task 4.3.2.b">🔗</a></div></article><div class="autopermalink" data-description="Exercise 4.3.2"><a href="#exercises-Confidence-Intervals-2" title="Copy heading and permalink for Exercise 4.3.2" aria-label="Copy heading and permalink for Exercise 4.3.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
<div class="para" id="exercises-Confidence-Intervals-3-1-1">The weights of five mice are measured and recorded below. Give a 95% confidence interval for the sample mean weight of mice. (Pretend 5 measurements is large enough for the CLT to apply.)<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> <figure class="table table-like" id="exercises-Confidence-Intervals-3-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2.1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 4.2.1: "><a href="#exercises-Confidence-Intervals-3-1-2" title="Copy heading and permalink for Table 4.2.1: " aria-label="Copy heading and permalink for Table 4.2.1: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
</div> <figure class="table table-like" id="exercises-Confidence-Intervals-3-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.3.1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 4.3.1: "><a href="#exercises-Confidence-Intervals-3-1-2" title="Copy heading and permalink for Table 4.3.1: " aria-label="Copy heading and permalink for Table 4.3.1: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
<tr class="header-horizontal">
<th scope="col" class="c m b0 r0 l0 t0 lines">mouse <span class="process-math">\(i\)</span>
</th>
@@ -329,9 +336,9 @@ eBookConfig.enable_chatcodes = false;
<td class="c m b0 r0 l0 t0 lines">20</td>
<td class="c m b0 r0 l0 t0 lines">29</td>
</tr>
</table></div></figure><div class="autopermalink" data-description="Exercise 4.2.3"><a href="#exercises-Confidence-Intervals-3" title="Copy heading and permalink for Exercise 4.2.3" aria-label="Copy heading and permalink for Exercise 4.2.3">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
</table></div></figure><div class="autopermalink" data-description="Exercise 4.3.3"><a href="#exercises-Confidence-Intervals-3" title="Copy heading and permalink for Exercise 4.3.3" aria-label="Copy heading and permalink for Exercise 4.3.3">🔗</a></div></article><article class="exercise exercise-like" id="exercises-Confidence-Intervals-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
<div class="para" id="exercises-Confidence-Intervals-4-1-1">The heights of five plants are measured and recorded below. Give a 95% confidence interval around the sample mean for the heights of the plants. (Pretend 5 measurements is large enough for the CLT to apply.)<div class="autopermalink" data-description="Paragraph"><a href="#exercises-Confidence-Intervals-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> <figure class="table table-like" id="exercises-Confidence-Intervals-4-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.2.2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 4.2.2: "><a href="#exercises-Confidence-Intervals-4-1-2" title="Copy heading and permalink for Table 4.2.2: " aria-label="Copy heading and permalink for Table 4.2.2: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
</div> <figure class="table table-like" id="exercises-Confidence-Intervals-4-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">4.3.2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 4.3.2: "><a href="#exercises-Confidence-Intervals-4-1-2" title="Copy heading and permalink for Table 4.3.2: " aria-label="Copy heading and permalink for Table 4.3.2: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
<tr class="header-horizontal">
<th scope="col" class="c m b0 r0 l0 t0 lines">plant <span class="process-math">\(i\)</span>
</th>
@@ -349,7 +356,7 @@ eBookConfig.enable_chatcodes = false;
<td class="c m b0 r0 l0 t0 lines">21</td>
<td class="c m b0 r0 l0 t0 lines">17</td>
</tr>
</table></div></figure><div class="autopermalink" data-description="Exercise 4.2.4"><a href="#exercises-Confidence-Intervals-4" title="Copy heading and permalink for Exercise 4.2.4" aria-label="Copy heading and permalink for Exercise 4.2.4">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.2"><a href="#exercises-Confidence-Intervals" title="Copy heading and permalink for Exercises 4.2" aria-label="Copy heading and permalink for Exercises 4.2">🔗</a></div></section><div class="autopermalink" data-description="Section 4.2: Confidence Intervals"><a href="#sec-Confidence-Intervals" title="Copy heading and permalink for Section 4.2: Confidence Intervals" aria-label="Copy heading and permalink for Section 4.2: Confidence Intervals">🔗</a></div></section></div>
</table></div></figure><div class="autopermalink" data-description="Exercise 4.3.4"><a href="#exercises-Confidence-Intervals-4" title="Copy heading and permalink for Exercise 4.3.4" aria-label="Copy heading and permalink for Exercise 4.3.4">🔗</a></div></article><div class="autopermalink" data-description="Exercises 4.3"><a href="#exercises-Confidence-Intervals" title="Copy heading and permalink for Exercises 4.3" aria-label="Copy heading and permalink for Exercises 4.3">🔗</a></div></section><div class="autopermalink" data-description="Section 4.3: Confidence Intervals"><a href="#sec-Confidence-Intervals" title="Copy heading and permalink for Section 4.3: Confidence Intervals" aria-label="Copy heading and permalink for Section 4.3: Confidence Intervals">🔗</a></div></section></div>
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