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<h1 class="heading"><a href="my-great-book.html"><span class="title">Math 1044 Notes</span></a></h1>
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<div class="toc-title-box"><a href="sec-Probability.html" class="internal"><span class="codenumber">1.2</span> <span class="title">Definition of Probability</span></a></div>
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<div class="toc-title-box"><a href="sec-Conditional-Probability.html" class="internal"><span class="codenumber">1.3</span> <span class="title">Conditional Probability</span></a></div>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Conditional-Probability.html#subsec-diagnostic-testing" class="internal"><span class="codenumber">1.3.2</span> <span class="title">Diagnostic Testing</span></a></div></li>
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<div class="toc-title-box"><a href="ch-Random-Variables.html" class="internal"><span class="codenumber">2</span> <span class="title">Random Variables</span></a></div>
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<div class="toc-title-box"><a href="sec-Discrete-RVs.html" class="internal"><span class="codenumber">2.1</span> <span class="title">Discrete Random Variables</span></a></div>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-binomial-distribution" class="internal"><span class="codenumber">2.1.2</span> <span class="title">The Binomial Distribution</span></a></div></li>
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<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="sec-Discrete-RVs.html#subsec-poisson-distribution" class="internal"><span class="codenumber">2.1.4</span> <span class="title">Poisson Distribution</span></a></div></li>
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<div class="toc-title-box"><a href="sec-Continuous-RVs.html" class="internal"><span class="codenumber">2.2</span> <span class="title">Continuous Random Variables</span></a></div>
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<div class="toc-title-box"><a href="sec-Joint-Distributions.html" class="internal"><span class="codenumber">2.3</span> <span class="title">Joint Distributions</span></a></div>
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<div class="toc-title-box"><a href="sec-Expected-Value.html" class="internal"><span class="codenumber">3.1</span> <span class="title">Expected Value</span></a></div>
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<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>
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<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>
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<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>
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<div class="toc-title-box"><a href="ch-Hypothesis-Testing.html" class="internal"><span class="codenumber">5</span> <span class="title">Hypothesis Testing</span></a></div>
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<div class="toc-title-box"><a href="sec-One-Sample-Tests.html" class="internal"><span class="codenumber">5.1</span> <span class="title">One Sample Tests</span></a></div>
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<ul class="structural toc-item-list active"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-One-Sample-Tests.html#exercises-One-Sample-Tests" class="internal"><span class="codenumber">5.1</span> <span class="title">Exercises</span></a></div></li></ul>
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<div class="toc-title-box"><a href="sec-Two-Sample-Tests.html" class="internal"><span class="codenumber">5.2</span> <span class="title">Two Sample Tests</span></a></div>
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<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Two-Sample-Tests.html#exercises-Two-Sample-Tests" class="internal"><span class="codenumber">5.2</span> <span class="title">Exercises</span></a></div></li></ul>
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<div class="toc-title-box"><a href="sec-Power.html" class="internal"><span class="codenumber">5.3</span> <span class="title">Power of a Test</span></a></div>
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<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Power.html#exercises-Power" class="internal"><span class="codenumber">5.3</span> <span class="title">Exercises</span></a></div></li></ul>
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<div class="toc-title-box"><a href="sec-Chi-Squared.html" class="internal"><span class="codenumber">5.4</span> <span class="title"><span class="process-math">\(\chi^2\)</span> Test</span></a></div>
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<ul class="structural toc-item-list"><li class="toc-item toc-exercises"><div class="toc-title-box"><a href="sec-Chi-Squared.html#exercises-Chi-Squared" class="internal"><span class="codenumber">5.4</span> <span class="title">Exercises</span></a></div></li></ul>
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<div class="toc-title-box"><a href="sec-Linear-Regression.html" class="internal"><span class="codenumber">6.2</span> <span class="title">Linear Regression</span></a></div>
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<div class="toc-title-box"><a href="backmatter-2.html" class="internal"><span class="codenumber">A</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table</span></a></div>
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<ul class="structural toc-item-list"><li class="toc-item toc-section"><div class="toc-title-box"><a href="app-Phi-table.html" class="internal"><span class="codenumber">A.1</span> <span class="title"><span class="process-math">\(\Phi(z)\)</span> Table of Values</span></a></div></li></ul>
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<main class="ptx-main"><div id="ptx-content" class="ptx-content"><section class="section" id="sec-One-Sample-Tests"><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">5.1</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="title">One Sample Tests</span>
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</h2>
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<div class="para" id="sec-One-Sample-Tests-2">Text of section.<div class="autopermalink" data-description="Paragraph"><a href="#sec-One-Sample-Tests-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<section class="exercises" id="exercises-One-Sample-Tests"><h3 class="heading hide-type">
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<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>
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</h3>
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<article class="exercise exercise-like" id="exercises-One-Sample-Tests-1"><h4 class="heading"><span class="codenumber">1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
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<div class="introduction" id="exercises-One-Sample-Tests-1-1"><div class="para" id="exercises-One-Sample-Tests-1-1-1">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="#exercises-One-Sample-Tests-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<article class="task exercise-like" id="exercises-One-Sample-Tests-1-2"><h5 class="heading"><span class="codenumber">(a)</span></h5>
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<div class="para" id="exercises-One-Sample-Tests-1-2-1-1">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="#exercises-One-Sample-Tests-1-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Task 5.1.1.a"><a href="#exercises-One-Sample-Tests-1-2" title="Copy heading and permalink for Task 5.1.1.a" aria-label="Copy heading and permalink for Task 5.1.1.a">🔗</a></div></article><article class="task exercise-like" id="exercises-One-Sample-Tests-1-3"><h5 class="heading"><span class="codenumber">(b)</span></h5>
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<div class="para" id="exercises-One-Sample-Tests-1-3-1-1">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="#exercises-One-Sample-Tests-1-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Task 5.1.1.b"><a href="#exercises-One-Sample-Tests-1-3" title="Copy heading and permalink for Task 5.1.1.b" aria-label="Copy heading and permalink for Task 5.1.1.b">🔗</a></div></article><article class="task exercise-like" id="exercises-One-Sample-Tests-1-4"><h5 class="heading"><span class="codenumber">(c)</span></h5>
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<div class="para" id="exercises-One-Sample-Tests-1-4-1-1">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="#exercises-One-Sample-Tests-1-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Task 5.1.1.c"><a href="#exercises-One-Sample-Tests-1-4" title="Copy heading and permalink for Task 5.1.1.c" aria-label="Copy heading and permalink for Task 5.1.1.c">🔗</a></div></article><article class="task exercise-like" id="exercises-One-Sample-Tests-1-5"><h5 class="heading"><span class="codenumber">(d)</span></h5>
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<div class="para" id="exercises-One-Sample-Tests-1-5-1-1">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="#exercises-One-Sample-Tests-1-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Task 5.1.1.d"><a href="#exercises-One-Sample-Tests-1-5" title="Copy heading and permalink for Task 5.1.1.d" aria-label="Copy heading and permalink for Task 5.1.1.d">🔗</a></div></article><div class="autopermalink" data-description="Exercise 5.1.1"><a href="#exercises-One-Sample-Tests-1" title="Copy heading and permalink for Exercise 5.1.1" aria-label="Copy heading and permalink for Exercise 5.1.1">🔗</a></div></article><article class="exercise exercise-like" id="exercises-One-Sample-Tests-2"><h4 class="heading"><span class="codenumber">2<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
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<div class="para" id="exercises-One-Sample-Tests-2-1-1">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="#exercises-One-Sample-Tests-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Exercise 5.1.2"><a href="#exercises-One-Sample-Tests-2" title="Copy heading and permalink for Exercise 5.1.2" aria-label="Copy heading and permalink for Exercise 5.1.2">🔗</a></div></article><article class="exercise exercise-like" id="exercises-One-Sample-Tests-3"><h4 class="heading"><span class="codenumber">3<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
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<div class="para" id="exercises-One-Sample-Tests-3-1-1">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="#exercises-One-Sample-Tests-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Exercise 5.1.3"><a href="#exercises-One-Sample-Tests-3" title="Copy heading and permalink for Exercise 5.1.3" aria-label="Copy heading and permalink for Exercise 5.1.3">🔗</a></div></article><article class="exercise exercise-like" id="exercises-One-Sample-Tests-4"><h4 class="heading"><span class="codenumber">4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
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<div class="para" id="exercises-One-Sample-Tests-4-1-1">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="#exercises-One-Sample-Tests-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Exercise 5.1.4"><a href="#exercises-One-Sample-Tests-4" title="Copy heading and permalink for Exercise 5.1.4" aria-label="Copy heading and permalink for Exercise 5.1.4">🔗</a></div></article><article class="exercise exercise-like" id="exercises-One-Sample-Tests-5"><h4 class="heading"><span class="codenumber">5<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
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<div class="para" id="exercises-One-Sample-Tests-5-1-1">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="#exercises-One-Sample-Tests-5-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Exercise 5.1.5"><a href="#exercises-One-Sample-Tests-5" title="Copy heading and permalink for Exercise 5.1.5" aria-label="Copy heading and permalink for Exercise 5.1.5">🔗</a></div></article><div class="autopermalink" data-description="Exercises 5.1"><a href="#exercises-One-Sample-Tests" title="Copy heading and permalink for Exercises 5.1" aria-label="Copy heading and permalink for Exercises 5.1">🔗</a></div></section><div class="autopermalink" data-description="Section 5.1: One Sample Tests"><a href="#sec-One-Sample-Tests" title="Copy heading and permalink for Section 5.1: One Sample Tests" aria-label="Copy heading and permalink for Section 5.1: One Sample Tests">🔗</a></div></section></div>
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