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<h1 class="heading"><a href="root-1-2.html"><span class="title">Introduction to Probability and Statistics for the Life Sciences</span> <span class="subtitle">Spring 2026 MATH 1044</span></a></h1>
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<div class="toc-title-box"><a href="notes-01-13.html" class="internal"><span class="title">Tuesday, Jan 13</span></a></div>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-13.html#subsec-Sets" class="internal"><span class="title">Sec 1.1: Sets</span></a></div></li>
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<div class="toc-title-box"><a href="notes-01-15.html" class="internal"><span class="title">Thursday, Jan 15</span></a></div>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-15.html#subsec-Conditional-Probability" class="internal"><span class="title">Sec 1.3: Conditional Probability</span></a></div></li>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-15.html#subsec-Independent-Events" class="internal"><span class="title">Sec 1.4: Independent Events</span></a></div></li>
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<div class="toc-title-box"><a href="notes-01-20.html" class="internal"><span class="title">Tuesday, Jan 20</span></a></div>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-20.html#subsec-hw1-review" class="internal"><span class="title">HW 1 Q5</span></a></div></li>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-20.html#subsec-Discrete-Random-Variables" class="internal"><span class="title">Sec 2.1: Random Variables</span></a></div></li>
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<div class="toc-title-box"><a href="notes-01-22.html" class="internal"><span class="title">Thursday, Jan 22</span></a></div>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-22.html#subsec-discrete-distributions" class="internal"><span class="title">Discrete Distributions</span></a></div></li>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-22.html#subsec-continuous-distributions" class="internal"><span class="title">Continuous Distributions</span></a></div></li>
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<div class="toc-title-box"><a href="notes-01-27.html" class="internal"><span class="title">Tuesday, Jan 27</span></a></div>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-27.html#subsec-continuous-2" class="internal"><span class="title">Continuous Distributions</span></a></div></li>
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<div class="toc-title-box"><a href="notes-01-29.html" class="internal"><span class="title">Thursday, Jan 29</span></a></div>
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<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-29.html#notes-01-29-3" class="internal"><span class="title">Expected Value</span></a></div></li></ul>
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<div class="toc-title-box"><a href="notes-02-03.html" class="internal"><span class="title">Tuesday, Feb 3</span></a></div>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-05.html#notes-02-05-3" class="internal"><span class="title">Summary</span></a></div></li>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-05.html#notes-02-05-4" class="internal"><span class="title">Covariance</span></a></div></li>
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<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-10.html#notes-02-10-3" class="internal"><span class="title">Likelihood</span></a></div></li></ul>
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<div class="toc-title-box"><a href="notes-02-19.html" class="internal"><span class="title">Thursday, Feb 19</span></a></div>
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<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-19.html#notes-02-19-3" class="internal"><span class="title">Central Limit Theorem</span></a></div></li></ul>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-24.html#notes-02-24-3" class="internal"><span class="title">More Central Limit Theorem</span></a></div></li>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-24.html#notes-02-24-4" class="internal"><span class="title">Confidence Intervals</span></a></div></li>
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<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="Exam-1-Review.html#Exam-1-Review-4" class="internal"><span class="title">Exercises</span></a></div></li>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="Exam-2-Review.html#Exam-2-Review-3" class="internal"><span class="title">Allowed Materials</span></a></div></li>
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<li class="toc-item toc-exercises"><div class="toc-title-box"><a href="Exam-2-Review.html#Exam-2-Review-4" class="internal"><span class="title">Exercises</span></a></div></li>
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<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="Exam-2-Review"><h2 class="heading hide-type">
|
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<span class="type">Section</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber"></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Exam 2 Review</span>
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</h2>
|
||
<section class="introduction" id="Exam-2-Review-2"><div class="para" id="Exam-2-Review-2-1">Use the following problems to prepare for the exam. There will be in-class review on Tuesday 3/31 and Thursday 4/2. Your recitation this week will also be exam review.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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</div></section><section class="subsection" id="Exam-2-Review-3"><h3 class="heading hide-type">
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||
<span class="type">Subsection</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber"></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Allowed Materials</span>
|
||
</h3>
|
||
<div class="para" id="Exam-2-Review-3-2">You will be allowed to use a scientific calculator (<em class="emphasis">not</em> a graphing calculator, <em class="emphasis">not</em> a calculator app on your phone). You may not share a calculator with another student; you must use your own calculator.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-3-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="para" id="Exam-2-Review-3-3">You may bring a standard 3 in x 5 in index card with prepared notes. You may use both sides of the notecard. You must put your full name in the top right corner of the card, and turn it in along with your exam.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-3-3" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
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</div>
|
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<div class="autopermalink" data-description="Subsection: Allowed Materials"><a href="#Exam-2-Review-3" title="Copy heading and permalink for Subsection: Allowed Materials" aria-label="Copy heading and permalink for Subsection: Allowed Materials">🔗</a></div></section><section class="exercises" id="Exam-2-Review-4"><h3 class="heading hide-type">
|
||
<span class="type">Exercises</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber"></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">Exercises</span>
|
||
</h3>
|
||
<article class="exercise exercise-like" id="Exam-2-Review-4-1"><h4 class="heading"><span class="codenumber">1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-1-1-1">Suppose a coin has probability 0.4 of coming up heads, and we flip the coin 100 times. Let <span class="process-math">\(S\)</span> be the number of heads. Estimate the probability that <span class="process-math">\(34 \leq S \leq 44\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="solutions"><details id="Exam-2-Review-4-1-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-1-2-1">
|
||
<span class="process-math">\(\Pr(34 \leq S \leq 44) \approx 0.8212 - 0.0918 = 0.7294.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-1-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 1.1"><a href="#Exam-2-Review-4-1-2" title="Copy heading and permalink for Answer 1.1" aria-label="Copy heading and permalink for Answer 1.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Exercise 1"><a href="#Exam-2-Review-4-1" title="Copy heading and permalink for Exercise 1" aria-label="Copy heading and permalink for Exercise 1">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-2-1-1">Suppose a fair die is rolled 100 times, and let <span class="process-math">\(m\)</span> be the average value of the rolls. Estimate the probability that <span class="process-math">\(3.45 \leq m \leq 3.55\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="solutions"><details id="Exam-2-Review-4-2-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-2-2-1">
|
||
<span class="process-math">\(\Pr(3.45 \leq m \leq 3.55) \approx 0.6255 - 0.3745 = 0.2510.\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 2.1"><a href="#Exam-2-Review-4-2-2" title="Copy heading and permalink for Answer 2.1" aria-label="Copy heading and permalink for Answer 2.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Exercise 2"><a href="#Exam-2-Review-4-2" title="Copy heading and permalink for Exercise 2" aria-label="Copy heading and permalink for Exercise 2">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="introduction" id="Exam-2-Review-4-3-1"><div class="para" id="Exam-2-Review-4-3-1-1">The heights of men in the US have a mean of 69 in and a variance of about 9 in<span class="process-math">\(^2\text{,}\)</span> and the heights of women in the US have a mean of 63.5 in with a variance of 6.25 in<span class="process-math">\(^2\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-3-1-1" 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="Exam-2-Review-4-3-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-3-2-1-1">Suppose the heights of 30 men are sampled, and a sample mean <span class="process-math">\(m\)</span> is taken. Find the expected value and variance of <span class="process-math">\(m\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-3-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="solutions"><details id="Exam-2-Review-4-3-2-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-3-2-2-1">
|
||
<span class="process-math">\(\E(m) = 69\)</span> and <span class="process-math">\(\Var(m) = 0.3\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-3-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 3.a.1"><a href="#Exam-2-Review-4-3-2-2" title="Copy heading and permalink for Answer 3.a.1" aria-label="Copy heading and permalink for Answer 3.a.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Task 3.a"><a href="#Exam-2-Review-4-3-2" title="Copy heading and permalink for Task 3.a" aria-label="Copy heading and permalink for Task 3.a">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-3-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-3-3-1-1">Estimate the probability that <span class="process-math">\(m \geq 69.5\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-3-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="solutions"><details id="Exam-2-Review-4-3-3-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-3-3-2-1">
|
||
<span class="process-math">\(\Pr(m \geq 69.5) \approx 1 - 0.8186 = 0.1814\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-3-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 3.b.1"><a href="#Exam-2-Review-4-3-3-2" title="Copy heading and permalink for Answer 3.b.1" aria-label="Copy heading and permalink for Answer 3.b.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Task 3.b"><a href="#Exam-2-Review-4-3-3" title="Copy heading and permalink for Task 3.b" aria-label="Copy heading and permalink for Task 3.b">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-3-4"><h5 class="heading"><span class="codenumber">(c)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-3-4-1-1">If the sampled group was women, estimate the probability that <span class="process-math">\(m \geq 64\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-3-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="solutions"><details id="Exam-2-Review-4-3-4-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-3-4-2-1">
|
||
<span class="process-math">\(\E(m) = 63.5\)</span> and <span class="process-math">\(\Var(m) \approx 0.208\text{.}\)</span> <span class="process-math">\(\Pr(m \geq 64) \approx 1 - 0.8643 = 0.1357\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-3-4-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 3.c.1"><a href="#Exam-2-Review-4-3-4-2" title="Copy heading and permalink for Answer 3.c.1" aria-label="Copy heading and permalink for Answer 3.c.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Task 3.c"><a href="#Exam-2-Review-4-3-4" title="Copy heading and permalink for Task 3.c" aria-label="Copy heading and permalink for Task 3.c">🔗</a></div></article><div class="autopermalink" data-description="Exercise 3"><a href="#Exam-2-Review-4-3" title="Copy heading and permalink for Exercise 3" aria-label="Copy heading and permalink for Exercise 3">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-4-1-1">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="#Exam-2-Review-4-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="solutions"><details id="Exam-2-Review-4-4-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-4-2-1">
|
||
<span class="process-math">\([0.504, 0.696]\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-4-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 4.1"><a href="#Exam-2-Review-4-4-2" title="Copy heading and permalink for Answer 4.1" aria-label="Copy heading and permalink for Answer 4.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Exercise 4"><a href="#Exam-2-Review-4-4" title="Copy heading and permalink for Exercise 4" aria-label="Copy heading and permalink for Exercise 4">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-5"><h4 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="introduction" id="Exam-2-Review-4-5-1"><div class="para" id="Exam-2-Review-4-5-1-1">Suppose in a sample of 100 people, 12 are left-handed.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-5-1-1" 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="Exam-2-Review-4-5-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-5-2-1-1">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="#Exam-2-Review-4-5-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="solutions"><details id="Exam-2-Review-4-5-2-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-5-2-2-1">
|
||
<span class="process-math">\([0.056, 0.184]\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-5-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 5.a.1"><a href="#Exam-2-Review-4-5-2-2" title="Copy heading and permalink for Answer 5.a.1" aria-label="Copy heading and permalink for Answer 5.a.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Task 5.a"><a href="#Exam-2-Review-4-5-2" title="Copy heading and permalink for Task 5.a" aria-label="Copy heading and permalink for Task 5.a">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-5-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-5-3-1-1">Give a 90% confidence interval.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-5-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="solutions"><details id="Exam-2-Review-4-5-3-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-5-3-2-1">
|
||
<span class="process-math">\([0.066, 0.174]\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-5-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 5.b.1"><a href="#Exam-2-Review-4-5-3-2" title="Copy heading and permalink for Answer 5.b.1" aria-label="Copy heading and permalink for Answer 5.b.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Task 5.b"><a href="#Exam-2-Review-4-5-3" title="Copy heading and permalink for Task 5.b" aria-label="Copy heading and permalink for Task 5.b">🔗</a></div></article><div class="autopermalink" data-description="Exercise 5"><a href="#Exam-2-Review-4-5" title="Copy heading and permalink for Exercise 5" aria-label="Copy heading and permalink for Exercise 5">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-6"><h4 class="heading"><span class="codenumber">6<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-6-1-1">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="#Exam-2-Review-4-6-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div> <figure class="table table-like" id="Exam-2-Review-4-6-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">136<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 136: "><a href="#Exam-2-Review-4-6-1-2" title="Copy heading and permalink for Table 136: " aria-label="Copy heading and permalink for Table 136: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
|
||
<tr class="header-horizontal">
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">mouse <span class="process-math">\(i\)</span>
|
||
</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">weight <span class="process-math">\(W_i\)</span> (g)</th>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">1</td>
|
||
<td class="c m b0 r0 l0 t0 lines">26</td>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">2</td>
|
||
<td class="c m b0 r0 l0 t0 lines">32</td>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">3</td>
|
||
<td class="c m b0 r0 l0 t0 lines">33</td>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">4</td>
|
||
<td class="c m b0 r0 l0 t0 lines">20</td>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">5</td>
|
||
<td class="c m b0 r0 l0 t0 lines">29</td>
|
||
</tr>
|
||
</table></div></figure><div class="solutions"><details id="Exam-2-Review-4-6-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-6-2-1"> <span class="process-math">\([23.39, 32.61]\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-6-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 6.1"><a href="#Exam-2-Review-4-6-2" title="Copy heading and permalink for Answer 6.1" aria-label="Copy heading and permalink for Answer 6.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Exercise 6"><a href="#Exam-2-Review-4-6" title="Copy heading and permalink for Exercise 6" aria-label="Copy heading and permalink for Exercise 6">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-7"><h4 class="heading"><span class="codenumber">7<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-7-1-1">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="#Exam-2-Review-4-7-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div> <figure class="table table-like" id="Exam-2-Review-4-7-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">137<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 137: "><a href="#Exam-2-Review-4-7-1-2" title="Copy heading and permalink for Table 137: " aria-label="Copy heading and permalink for Table 137: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
|
||
<tr class="header-horizontal">
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">plant <span class="process-math">\(i\)</span>
|
||
</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">height <span class="process-math">\(H_i\)</span> (in)</th>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">1</td>
|
||
<td class="c m b0 r0 l0 t0 lines">15</td>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">2</td>
|
||
<td class="c m b0 r0 l0 t0 lines">14</td>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">3</td>
|
||
<td class="c m b0 r0 l0 t0 lines">18</td>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">4</td>
|
||
<td class="c m b0 r0 l0 t0 lines">21</td>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">5</td>
|
||
<td class="c m b0 r0 l0 t0 lines">17</td>
|
||
</tr>
|
||
</table></div></figure><div class="solutions"><details id="Exam-2-Review-4-7-2" class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="answer solution-like knowl__content">
|
||
<div class="para" id="Exam-2-Review-4-7-2-1"> <span class="process-math">\([14.61, 19.39]\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-7-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Answer 7.1"><a href="#Exam-2-Review-4-7-2" title="Copy heading and permalink for Answer 7.1" aria-label="Copy heading and permalink for Answer 7.1">🔗</a></div>
|
||
</div></details></div>
|
||
<div class="autopermalink" data-description="Exercise 7"><a href="#Exam-2-Review-4-7" title="Copy heading and permalink for Exercise 7" aria-label="Copy heading and permalink for Exercise 7">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-8"><h4 class="heading"><span class="codenumber">8<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="introduction" id="Exam-2-Review-4-8-1"><div class="para" id="Exam-2-Review-4-8-1-1">In each of the following scenarios, determine whether we should use a 1-tailed test or a 2-tailed test.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-8-1-1" 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="Exam-2-Review-4-8-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-8-2-1-1">We have a coin which we’ve flipped many times, seeing an above-average number of heads. We suspect the coin comes up heads more often than a fair coin would.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-8-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 8.a"><a href="#Exam-2-Review-4-8-2" title="Copy heading and permalink for Task 8.a" aria-label="Copy heading and permalink for Task 8.a">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-8-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-8-3-1-1">We find a coin on the street and wonder whether or not it’s a fair coin.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-8-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 8.b"><a href="#Exam-2-Review-4-8-3" title="Copy heading and permalink for Task 8.b" aria-label="Copy heading and permalink for Task 8.b">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-8-4"><h5 class="heading"><span class="codenumber">(c)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-8-4-1-1">We suspect there will be a difference in average weight of mice caught during the summer versus during the winter.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-8-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 8.c"><a href="#Exam-2-Review-4-8-4" title="Copy heading and permalink for Task 8.c" aria-label="Copy heading and permalink for Task 8.c">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-8-5"><h5 class="heading"><span class="codenumber">(d)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-8-5-1-1">In a medical study, a group of patients are gathered and the proportion experiencing particular symptoms is measured. A new drug intended to eliminate these symptoms is administered, after which the proportion experiencing symptoms is measured again.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-8-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 8.d"><a href="#Exam-2-Review-4-8-5" title="Copy heading and permalink for Task 8.d" aria-label="Copy heading and permalink for Task 8.d">🔗</a></div></article><div class="autopermalink" data-description="Exercise 8"><a href="#Exam-2-Review-4-8" title="Copy heading and permalink for Exercise 8" aria-label="Copy heading and permalink for Exercise 8">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-9"><h4 class="heading"><span class="codenumber">9<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-9-1-1">Suppose we find a coin and wonder whether it’s fair. As a first test, we decide to flip the coin 200 times and count the number of heads. If we see 112 heads, should we accept or reject the null hypothesis of a fair coin at a significance level of 0.05?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-9-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Exercise 9"><a href="#Exam-2-Review-4-9" title="Copy heading and permalink for Exercise 9" aria-label="Copy heading and permalink for Exercise 9">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-10"><h4 class="heading"><span class="codenumber">10<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-10-1-1">Suppose we have a coin which we suspect comes up heads more often than a fair coin would. As a first test, we decide to flip the coin 200 times and count the number of heads. If we see 112 heads, should we accept or reject the null hypothesis of a fair coin at a significance level of 0.05?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-10-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Exercise 10"><a href="#Exam-2-Review-4-10" title="Copy heading and permalink for Exercise 10" aria-label="Copy heading and permalink for Exercise 10">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-11"><h4 class="heading"><span class="codenumber">11<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-11-1-1">Suppose we find a six-sided die and wonder whether it’s fair. As a first test, we decide to roll the die 100 times and count the number of times it comes up 1. If we roll 22 1’s, should we accept or reject the null hypothesis of a fair die at a significance level of 0.05?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-11-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Exercise 11"><a href="#Exam-2-Review-4-11" title="Copy heading and permalink for Exercise 11" aria-label="Copy heading and permalink for Exercise 11">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-12"><h4 class="heading"><span class="codenumber">12<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-12-1-1">Suppose a particular plant when grown outdoors has an average height of 39 in with a variance of 20 in<span class="process-math">\(^2\text{.}\)</span> We suspect that growing this plant in a greenhouse will increase its height. A sample of 50 plants grown in a greenhouse has an average height of 40 in. Is this significant enough data to reject the null hypothesis of equal means at the <span class="process-math">\(p = 0.05\)</span> significance level?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-12-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Exercise 12"><a href="#Exam-2-Review-4-12" title="Copy heading and permalink for Exercise 12" aria-label="Copy heading and permalink for Exercise 12">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-13"><h4 class="heading"><span class="codenumber">13<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-13-1-1">A farmer is testing an experimental new plant fertilizer that is supposed to increase the weight of a particular apple variety. A control sample of 25 apples grown using the usual fertilizer have a mean weight of 75 grams and a sample variance of 90 grams<span class="process-math">\(^2\)</span> (for an individual apple). An experimental sample of 25 apples grown using the new fertilizer have a mean weight of 79 grams and a sample variance of 90 grams<span class="process-math">\(^2\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-13-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Exercise 13"><a href="#Exam-2-Review-4-13" title="Copy heading and permalink for Exercise 13" aria-label="Copy heading and permalink for Exercise 13">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-14"><h4 class="heading"><span class="codenumber">14<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-14-1-1">We have an established factory which produces coins that are close to fair. We’re opening up a second factory, and we’d like to ensure the machines are calibrated to produce coins which behave similarly to the ones produced in the established factory. We pick one sample coin from each factory, and flip each sample coin 100 times. The coin from the established factory flips 52 heads in 100 flips. The coin from the new factory flips 62 heads in 100 flips. Is this strong enough evidence to reject the null hypothesis that the two factories produce similar coins at a 0.05 significance level?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-14-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Exercise 14"><a href="#Exam-2-Review-4-14" title="Copy heading and permalink for Exercise 14" aria-label="Copy heading and permalink for Exercise 14">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-15"><h4 class="heading"><span class="codenumber">15<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-15-1-1">Suppose we find a coin and wonder whether it’s fair. As a first test, we decide to flip the coin 200 times and count the number of heads, <span class="process-math">\(S\text{.}\)</span> What values of <span class="process-math">\(S\)</span> would be extreme enough to reject the null hypothesis of a fair coin? If the coin actually has a 0.6 probability of coming up heads, what is the power of this test?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-15-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Exercise 15"><a href="#Exam-2-Review-4-15" title="Copy heading and permalink for Exercise 15" aria-label="Copy heading and permalink for Exercise 15">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-16"><h4 class="heading"><span class="codenumber">16<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-16-1-1">Suppose we have a coin which we suspect comes up heads more often than a fair coin would. As a first test, we decide to flip the coin 200 times and count the number of heads, <span class="process-math">\(S\text{.}\)</span> What values of <span class="process-math">\(S\)</span> would be extreme enough to reject the null hypothesis of a fair coin? If the coin actually has a 0.6 probability of coming up heads, what is the power of this test?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-16-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Exercise 16"><a href="#Exam-2-Review-4-16" title="Copy heading and permalink for Exercise 16" aria-label="Copy heading and permalink for Exercise 16">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-17"><h4 class="heading"><span class="codenumber">17<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="introduction" id="Exam-2-Review-4-17-1"><div class="para" id="Exam-2-Review-4-17-1-1">Suppose we find a six-sided die and wonder whether it’s fair. As a first test, we decide to roll the die 100 times and count the number of times it comes up 1. The expected number of 1’s is 50/3, with a variance of 125/9.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-17-1-1" 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="Exam-2-Review-4-17-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-17-2-1-1">Using a normal approximation, what is the smallest number of 1’s greater than 50/3 that would be extreme enough to reject the null hypothesis of a fair die?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-17-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 17.a"><a href="#Exam-2-Review-4-17-2" title="Copy heading and permalink for Task 17.a" aria-label="Copy heading and permalink for Task 17.a">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-17-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-17-3-1-1">Using a normal approximation, what is the greatest number of 1’s less than 50/3 that would be extreme enough to reject the null hypothesis of a fair die?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-17-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 17.b"><a href="#Exam-2-Review-4-17-3" title="Copy heading and permalink for Task 17.b" aria-label="Copy heading and permalink for Task 17.b">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-17-4"><h5 class="heading"><span class="codenumber">(c)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-17-4-1-1">Suppose that this die is weighted so that it rolls a 1 with probability 0.2. What would be the power of our test?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-17-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 17.c"><a href="#Exam-2-Review-4-17-4" title="Copy heading and permalink for Task 17.c" aria-label="Copy heading and permalink for Task 17.c">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-17-5"><h5 class="heading"><span class="codenumber">(d)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-17-5-1-1">Suppose we roll the die 100 times and see 23 1’s. Use the maximum likelihood value for the probability of rolling a 1 to calculate the power of the test.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-17-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 17.d"><a href="#Exam-2-Review-4-17-5" title="Copy heading and permalink for Task 17.d" aria-label="Copy heading and permalink for Task 17.d">🔗</a></div></article><div class="autopermalink" data-description="Exercise 17"><a href="#Exam-2-Review-4-17" title="Copy heading and permalink for Exercise 17" aria-label="Copy heading and permalink for Exercise 17">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-18"><h4 class="heading"><span class="codenumber">18<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-18-1-1">Suppose a particular plant when grown outdoors has an average height of 39 in with a variance of 20 in<span class="process-math">\(^2\text{.}\)</span> We suspect that growing this plant in a greenhouse will increase its height. We take the average height of a sample of 50 plants grown in a greenhouse. What is the minimum average height of this sample that would be extreme enough to reject the null hypothesis of equal means at the <span class="process-math">\(p = 0.05\)</span> significance level? If the plants, when grown in a greenhouse, would truly have an average height of 41 in, what is the power of our test?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-18-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Exercise 18"><a href="#Exam-2-Review-4-18" title="Copy heading and permalink for Exercise 18" aria-label="Copy heading and permalink for Exercise 18">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-19"><h4 class="heading"><span class="codenumber">19<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="para" id="Exam-2-Review-4-19-1-1">A store owner wants to determine how much shelf space to allocate to each of the drinks that they sell. They survey their customers about their favorite drinks. Is the data below consistent with the null hypothesis that each type of drink will be equally preferred?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-19-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div> <figure class="table table-like" id="Exam-2-Review-4-19-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">138<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 138: "><a href="#Exam-2-Review-4-19-1-2" title="Copy heading and permalink for Table 138: " aria-label="Copy heading and permalink for Table 138: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
|
||
<tr class="header-horizontal">
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">drink type</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">water</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">soda</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">tea</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">coffee</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">energy drinks</th>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines">favorite</td>
|
||
<td class="c m b0 r0 l0 t0 lines">28</td>
|
||
<td class="c m b0 r0 l0 t0 lines">17</td>
|
||
<td class="c m b0 r0 l0 t0 lines">15</td>
|
||
<td class="c m b0 r0 l0 t0 lines">26</td>
|
||
<td class="c m b0 r0 l0 t0 lines">14</td>
|
||
</tr>
|
||
</table></div></figure><div class="autopermalink" data-description="Exercise 19"><a href="#Exam-2-Review-4-19" title="Copy heading and permalink for Exercise 19" aria-label="Copy heading and permalink for Exercise 19">🔗</a></div></article><article class="exercise exercise-like" id="Exam-2-Review-4-20"><h4 class="heading"><span class="codenumber">20<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
|
||
<div class="introduction" id="Exam-2-Review-4-20-1">
|
||
<div class="para" id="Exam-2-Review-4-20-1-1">A particular drug is administered in 100 independent trials. In each trial, the drug is administered to four people, and we count how many respond to the drug. The table below shows how many trials have each different count of people who respond to the drug.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-20-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<figure class="table table-like" id="Exam-2-Review-4-20-1-2"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">139<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 139: "><a href="#Exam-2-Review-4-20-1-2" title="Copy heading and permalink for Table 139: " aria-label="Copy heading and permalink for Table 139: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
|
||
<tr class="header-horizontal">
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines"># who respond to drug</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">0</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">1</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">2</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">3</th>
|
||
<th scope="col" class="c m b1 r0 l0 t0 lines">4</th>
|
||
</tr>
|
||
<tr>
|
||
<td class="c m b0 r0 l0 t0 lines"># of trials</td>
|
||
<td class="c m b0 r0 l0 t0 lines">3</td>
|
||
<td class="c m b0 r0 l0 t0 lines">11</td>
|
||
<td class="c m b0 r0 l0 t0 lines">31</td>
|
||
<td class="c m b0 r0 l0 t0 lines">34</td>
|
||
<td class="c m b0 r0 l0 t0 lines">21</td>
|
||
</tr>
|
||
</table></div></figure>
|
||
</div>
|
||
<article class="task exercise-like" id="Exam-2-Review-4-20-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-20-2-1-1">Is the data consistent with a binomial distribution with parameter <span class="process-math">\(\theta = 0.7\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-20-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 20.a"><a href="#Exam-2-Review-4-20-2" title="Copy heading and permalink for Task 20.a" aria-label="Copy heading and permalink for Task 20.a">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-20-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-20-3-1-1">What is the total number of people who have been administered the drug? What is the total number who have responded to it? What is the maximum likelihood estimation <span class="process-math">\(\widehat{\theta}\)</span> for the probability that a person will respond to the drug?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-20-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
|
||
<div class="autopermalink" data-description="Task 20.b"><a href="#Exam-2-Review-4-20-3" title="Copy heading and permalink for Task 20.b" aria-label="Copy heading and permalink for Task 20.b">🔗</a></div></article><article class="task exercise-like" id="Exam-2-Review-4-20-4"><h5 class="heading"><span class="codenumber">(c)</span></h5>
|
||
<div class="para" id="Exam-2-Review-4-20-4-1-1">Is the data consistent with a binomial distribution with the MLE value of <span class="process-math">\(\widehat{\theta}\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-2-Review-4-20-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
|
||
</div>
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||
<div class="autopermalink" data-description="Task 20.c"><a href="#Exam-2-Review-4-20-4" title="Copy heading and permalink for Task 20.c" aria-label="Copy heading and permalink for Task 20.c">🔗</a></div></article><div class="autopermalink" data-description="Exercise 20"><a href="#Exam-2-Review-4-20" title="Copy heading and permalink for Exercise 20" aria-label="Copy heading and permalink for Exercise 20">🔗</a></div></article><div class="autopermalink" data-description="Exercises"><a href="#Exam-2-Review-4" title="Copy heading and permalink for Exercises" aria-label="Copy heading and permalink for Exercises">🔗</a></div></section><div class="autopermalink" data-description="Section: Exam 2 Review"><a href="#Exam-2-Review" title="Copy heading and permalink for Section: Exam 2 Review" aria-label="Copy heading and permalink for Section: Exam 2 Review">🔗</a></div></section></div>
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