Latest build deployed.

course/.mapping.json

@@ -1 +1 @@
-{"source/main.ptx": ["frontmatter", "course-documents", "ch-notes", "quizzes", "exams", "recitations", "review", "fun"], "source/syllabus/syllabus.ptx": ["syllabus"], "source/notes/1-13.ptx": ["notes-01-13"], "source/notes/1-15.ptx": ["notes-01-15"], "source/notes/1-20.ptx": ["notes-01-20"], "source/notes/1-22.ptx": ["notes-01-22"], "source/notes/1-27.ptx": ["notes-01-27"], "source/notes/1-29.ptx": ["notes-01-29"], "source/notes/2-3.ptx": ["notes-02-03"], "source/notes/2-5.ptx": ["notes-02-05"], "source/notes/2-10.ptx": ["notes-02-10"], "source/notes/2-19.ptx": ["notes-02-19"], "source/notes/2-24.ptx": ["notes-02-24"], "source/quizzes/quiz-01.ptx": ["quiz-01"], "source/quizzes/quiz-02.ptx": ["quiz-02"], "source/quizzes/quiz-03.ptx": ["quiz-03"], "source/exams/exam-01.ptx": ["exam-01"], "source/recitations/calculus-review.ptx": ["recitation-calculus-review"], "source/review/Exam-1-Review.ptx": ["Exam-1-Review"], "source/fun/boxes.ptx": ["boxes"]}
+{"source/main.ptx": ["frontmatter", "course-documents", "ch-notes", "quizzes", "exams", "recitations", "review", "fun"], "source/syllabus/syllabus.ptx": ["syllabus"], "source/notes/1-13.ptx": ["notes-01-13"], "source/notes/1-15.ptx": ["notes-01-15"], "source/notes/1-20.ptx": ["notes-01-20"], "source/notes/1-22.ptx": ["notes-01-22"], "source/notes/1-27.ptx": ["notes-01-27"], "source/notes/1-29.ptx": ["notes-01-29"], "source/notes/2-3.ptx": ["notes-02-03"], "source/notes/2-5.ptx": ["notes-02-05"], "source/notes/2-10.ptx": ["notes-02-10"], "source/notes/2-19.ptx": ["notes-02-19"], "source/notes/2-24.ptx": ["notes-02-24"], "source/quizzes/quiz-01.ptx": ["quiz-01"], "source/quizzes/quiz-02.ptx": ["quiz-02"], "source/quizzes/quiz-03.ptx": ["quiz-03"], "source/quizzes/quiz-04.ptx": ["quiz-04"], "source/exams/exam-01.ptx": ["exam-01"], "source/recitations/calculus-review.ptx": ["recitation-calculus-review"], "source/review/Exam-1-Review.ptx": ["Exam-1-Review"], "source/fun/boxes.ptx": ["boxes"]}

course/Exam-1-Review.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
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 </li>
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course/boxes.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/ch-notes.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-02.html" class="internal"><span class="title">Quiz 2</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/course-documents.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-02.html" class="internal"><span class="title">Quiz 2</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/exam-01.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
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course/exams.html

@@ -135,7 +135,7 @@ eBookConfig.enable_chatcodes =  false;
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+<button id="light-dark-button" class="light-dark-button button" title="Dark Mode"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe51c;</span><span class="name">Dark Mode</span></button></span><span class="treebuttons"><a class="previous-button button" href="quiz-04.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="up-button button" href="root-1-2.html" title="Up"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Up</span></a><a class="next-button button" href="exam-01.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a></span>
 </div></nav><div id="latex-macros" class="hidden-content process-math" style="display:none"><span class="process-math">\(\newcommand{\N}{\mathbb N}
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@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
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 </li>
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@@ -281,7 +282,7 @@ eBookConfig.enable_chatcodes =  false;
 </h2>
 <nav class="summary-links"><ul><li><a href="exam-01.html" class="internal"><span class="title">Exam 1</span></a></li></ul></nav><div class="autopermalink" data-description="Chapter: Exams"><a href="#exams" title="Copy heading and permalink for Chapter: Exams" aria-label="Copy heading and permalink for Chapter: Exams">🔗</a></div></section></div>
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+<a class="previous-button button" href="quiz-04.html" title="Previous"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cb;</span><span class="name">Prev</span></a><a class="top-button button" href="#" title="Top"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5ce;</span><span class="name">Top</span></a><a class="next-button button" href="exam-01.html" title="Next"><span class="name">Next</span><span class="icon material-symbols-outlined" aria-hidden="true">&#xe5cc;</span></a>
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course/frontmatter.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/fun.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
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course/index.html

@@ -2,7 +2,7 @@
 <html>
 <!--********************************************-->
 <!--*       Generated from PreTeXt source      *-->
-<!--*       on 2026-03-17T11:30:19-04:00       *-->
+<!--*       on 2026-03-26T09:51:41-04:00       *-->
 <!--*   A recent stable commit (2022-07-01):   *-->
 <!--* 6c761d3dba23af92cba35001c852aac04ae99a5f *-->
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course/lunr-pretext-search-index.js

@@ -1179,6 +1179,24 @@ var ptx_lunr_docs = [
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   "body": " Values     0.00  0.01  0.02  0.03  0.04  0.05  0.06  0.07  0.08  0.09    −1.6  0.0548  0.0537  0.0526  0.0516  0.0505  0.0495  0.0485  0.0475  0.0465  0.0455    −1.5  0.0668  0.0655  0.0643  0.0630  0.0618  0.0606  0.0594  0.0582  0.0571  0.0559    −1.4  0.0808  0.0793  0.0778  0.0764  0.0749  0.0735  0.0721  0.0708  0.0694  0.0681    −1.3  0.0968  0.0951  0.0934  0.0918  0.0901  0.0885  0.0869  0.0853  0.0838  0.0823    −1.2  0.1151  0.1131  0.1112  0.1093  0.1075  0.1056  0.1038  0.1020  0.1003  0.0985    0.2  0.5793  0.5832  0.5871  0.5910  0.5948  0.5987  0.6026  0.6064  0.6103  0.6141    0.3  0.6179  0.6217  0.6255  0.6293  0.6331  0.6368  0.6406  0.6443  0.6480  0.6517    0.4  0.6554  0.6591  0.6628  0.6664  0.6700  0.6736  0.6772  0.6808  0.6844  0.6879    0.5  0.6915  0.6950  0.6985  0.7019  0.7054  0.7088  0.7123  0.7157  0.7190  0.7224    0.6  0.7257  0.7291  0.7324  0.7357  0.7389  0.7422  0.7454  0.7486  0.7517  0.7549    "
 },
+{
+  "id": "quiz-04",
+  "level": "1",
+  "url": "quiz-04.html",
+  "type": "Worksheet",
+  "number": "",
+  "title": "Quiz 4",
+  "body": " Quiz 4    The following work should be completed individually. Use of notes or textbooks is not allowed. You may use a scientific calculator, not a graphing calculator or phone app.  Show all work unless instructed otherwise.       Suppose we have a coin that we're told is not fair and has a probability of of coming up heads. We suspect the probability is even higher than this.  Throughout the following parts, do not use a normal approximation.     We flip the coin 10 times and see 9 heads. Should we use a 1-tailed test or a 2-tailed test? Find the -value. Do we have strong enough evidence to reject the null hypothesis at a 0.05 significance level?    Using a 1-tailed test, the -value is : The -value is the sum: , so we can reject the null hypothesis.      What is the minimum number of heads we would need to see in 10 flips to reject the null hypothesis?    We saw in part (a) that at least 9 heads is enough to reject. Then: Adding to the previous probabilities, . So 8 heads would not be enough to reject the null hypothesis, therefore the minimum number of heads to reject would be 9.      What is the power of the test if the true value of the parameter is ?    With : So the power of the test is .      "
+},
+{
+  "id": "quiz-04-3-1",
+  "level": "2",
+  "url": "quiz-04.html#quiz-04-3-1",
+  "type": "Worksheet Exercise",
+  "number": "1",
+  "title": "",
+  "body": "  Suppose we have a coin that we're told is not fair and has a probability of of coming up heads. We suspect the probability is even higher than this.  Throughout the following parts, do not use a normal approximation.     We flip the coin 10 times and see 9 heads. Should we use a 1-tailed test or a 2-tailed test? Find the -value. Do we have strong enough evidence to reject the null hypothesis at a 0.05 significance level?    Using a 1-tailed test, the -value is : The -value is the sum: , so we can reject the null hypothesis.      What is the minimum number of heads we would need to see in 10 flips to reject the null hypothesis?    We saw in part (a) that at least 9 heads is enough to reject. Then: Adding to the previous probabilities, . So 8 heads would not be enough to reject the null hypothesis, therefore the minimum number of heads to reject would be 9.      What is the power of the test if the true value of the parameter is ?    With : So the power of the test is .    "
+},
 {
   "id": "exam-01",
   "level": "1",

course/notes-01-13.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/notes-01-15.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
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 </li>
 <li class="toc-item toc-chapter">

course/notes-01-20.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/notes-01-22.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/notes-01-27.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/notes-01-29.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/notes-02-03.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/notes-02-05.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
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 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/notes-02-10.html

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course/notes-02-24.html

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course/quiz-02.html

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+<p class="byline">Andy Eisenberg</p>
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+<li class="toc-item toc-chapter">
+<div class="toc-title-box"><a href="ch-notes.html" class="internal"><span class="title">Class Notes</span></a></div>
+<ul class="structural toc-item-list">
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-13.html" class="internal"><span class="title">Tuesday, Jan 13</span></a></div>
+<ul class="structural toc-item-list">
+<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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+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-15.html" class="internal"><span class="title">Thursday, Jan 15</span></a></div>
+<ul class="structural toc-item-list">
+<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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+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-20.html" class="internal"><span class="title">Tuesday, Jan 20</span></a></div>
+<ul class="structural toc-item-list">
+<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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+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-22.html" class="internal"><span class="title">Thursday, Jan 22</span></a></div>
+<ul class="structural toc-item-list">
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+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-27.html" class="internal"><span class="title">Tuesday, Jan 27</span></a></div>
+<ul class="structural toc-item-list">
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+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-01-29.html" class="internal"><span class="title">Thursday, Jan 29</span></a></div>
+<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>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-05.html" class="internal"><span class="title">Thursday, Feb 5</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>
+<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>
+</ul>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-10.html" class="internal"><span class="title">Tuesday, Feb 10</span></a></div>
+<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>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-19.html" class="internal"><span class="title">Thursday, Feb 19</span></a></div>
+<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>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-24.html" class="internal"><span class="title">Tuesday, Feb 24</span></a></div>
+<ul class="structural toc-item-list">
+<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>
+<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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+<section class="worksheet" id="quiz-04" data-margins="0.5in 0.5in 0.5in 0.5in"><h2 class="heading hide-type">
+<span class="type">Worksheet</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">Quiz 4</span><div class="print-links"><a href="?printpreview=quiz-04" class="print-link" title="Print preview"><span class="icon material-symbols-outlined" aria-hidden="true">&#xe8ad;</span></a></div>
+</h2>
+<section class="introduction" id="quiz-04-2"><div class="para" id="quiz-04-2-1">The following work should be completed individually. Use of notes or textbooks is not allowed. You may use a scientific calculator, not a graphing calculator or phone app.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="para" id="quiz-04-2-2">Show all work unless instructed otherwise.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-2-2" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div></section><section class="onepage" id="quiz-04-3"><article class="exercise exercise-like" id="quiz-04-3-1"><h3 class="heading"><span class="codenumber">1<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h3>
+<div class="introduction" id="quiz-04-3-1-1">
+<div class="para" id="quiz-04-3-1-1-1">Suppose we have a coin that we’re told is not fair and has a probability of <span class="process-math">\(\theta = 0.6\)</span> of coming up heads. We suspect the probability is even higher than this.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-3-1-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="para" id="quiz-04-3-1-1-2">Throughout the following parts, do <em class="emphasis">not</em> use a normal approximation.<div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-3-1-1-2" 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="quiz-04-3-1-2"><h4 class="heading"><span class="codenumber">(a)</span></h4>
+<div class="para" id="quiz-04-3-1-2-1-1">We flip the coin 10 times and see 9 heads. Should we use a 1-tailed test or a 2-tailed test? Find the <span class="process-math">\(p\)</span>-value. Do we have strong enough evidence to reject the null hypothesis at a 0.05 significance level?<div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-3-1-2-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="quiz-04-3-1-2-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
+<div class="para logical" id="quiz-04-3-1-2-2-1">
+<div class="para">Using a 1-tailed test, the <span class="process-math">\(p\)</span>-value is <span class="process-math">\(\Pr( \geq 9 \text{ heads})\text{:}\)</span>
+</div>
+<div class="displaymath process-math" id="quiz-04-3-1-2-2-1-3">
+\begin{align*}
+\Pr(9 \text{ heads}) \amp = {10 \choose 9} (0.6)^9 (1 - 0.6)^{10 - 9} = 10(0.6)^9(0.4)^1 \approx 0.04 \\
+\Pr(10 \text{ heads}) \amp = {10 \choose 10} (0.6)^{10} (1 - 0.6)^{10 - 10} = 1(0.6)^{10}(0.4)^{0} \approx 0.006 
+\end{align*}
+</div>
+<div class="para">The <span class="process-math">\(p\)</span>-value is the sum: <span class="process-math">\(\Pr(\geq 9 \text{ heads}) \approx 0.046 \lt 0.05\text{,}\)</span> so we can reject the null hypothesis.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-3-1-2-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 1.a.1"><a href="#quiz-04-3-1-2-2" title="Copy heading and permalink for Solution 1.a.1" aria-label="Copy heading and permalink for Solution 1.a.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 1.a"><a href="#quiz-04-3-1-2" title="Copy heading and permalink for Task 1.a" aria-label="Copy heading and permalink for Task 1.a">🔗</a></div></article><article class="task exercise-like" id="quiz-04-3-1-3"><h4 class="heading"><span class="codenumber">(b)</span></h4>
+<div class="para" id="quiz-04-3-1-3-1-1">What is the minimum number of heads we would need to see in 10 flips to reject the null hypothesis?<div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-3-1-3-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="quiz-04-3-1-3-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
+<div class="para logical" id="quiz-04-3-1-3-2-1">
+<div class="para">We saw in part (a) that at least 9 heads is enough to reject. Then:</div>
+<div class="displaymath process-math" id="quiz-04-3-1-3-2-1-1">
+\begin{gather*}
+\Pr(8 \text{ heads}) = {10 \choose 8} (0.6)^8 (1 - 0.6)^{10 - 8} = 45(0.6)^8(0.4)^2 \approx 0.121 
+\end{gather*}
+</div>
+<div class="para">Adding to the previous probabilities, <span class="process-math">\(\Pr(\geq 8 \text{ heads}) \approx 0.046 + 0.121 = 0.167 \gt 0.05\text{.}\)</span> So 8 heads would not be enough to reject the null hypothesis, therefore the minimum number of heads to reject would be 9.</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-3-1-3-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Solution 1.b.1"><a href="#quiz-04-3-1-3-2" title="Copy heading and permalink for Solution 1.b.1" aria-label="Copy heading and permalink for Solution 1.b.1">🔗</a></div>
+</div></details></div>
+<div class="autopermalink" data-description="Task 1.b"><a href="#quiz-04-3-1-3" title="Copy heading and permalink for Task 1.b" aria-label="Copy heading and permalink for Task 1.b">🔗</a></div></article><article class="task exercise-like" id="quiz-04-3-1-4"><h4 class="heading"><span class="codenumber">(c)</span></h4>
+<div class="para" id="quiz-04-3-1-4-1-1">What is the power of the test if the true value of the parameter is <span class="process-math">\(\theta = 0.8\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-3-1-4-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="solutions"><details id="quiz-04-3-1-4-2" class="solution solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Solution</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary><div class="solution solution-like knowl__content">
+<div class="para logical" id="quiz-04-3-1-4-2-1">
+<div class="para">With <span class="process-math">\(\theta = 0.8\text{:}\)</span>
+</div>
+<div class="displaymath process-math" id="quiz-04-3-1-4-2-1-2">
+\begin{align*}
+\Pr(9 \text{ heads}) \amp = {10 \choose 9} (0.8)^9 (1 - 0.8)^{10 - 9} = 10(0.8)^9(0.2)^1 \approx 0.268 \\
+\Pr(10 \text{ heads}) \amp = {10 \choose 10} (0.8)^{10} (1 - 0.8)^{10 - 10} = 1(0.8)^{10}(0.2)^{0} \approx 0.107 
+\end{align*}
+</div>
+<div class="para">So the power of the test is <span class="process-math">\(0.268 + 0.107 = 0.375\text{.}\)</span>
+</div>
+<div class="autopermalink" data-description="Paragraph"><a href="#quiz-04-3-1-4-2-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
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+</div></details></div>
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course/quizzes.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
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course/recitation-calculus-review.html

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course/recitations.html

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course/review.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-02.html" class="internal"><span class="title">Quiz 2</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/root-1-2.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-02.html" class="internal"><span class="title">Quiz 2</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">

course/syllabus.html

@@ -251,6 +251,7 @@ eBookConfig.enable_chatcodes =  false;
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-01.html" class="internal"><span class="title">Quiz 1</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-02.html" class="internal"><span class="title">Quiz 2</span></a></div></li>
 <li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-03.html" class="internal"><span class="title">Quiz 3</span></a></div></li>
+<li class="toc-item toc-worksheet"><div class="toc-title-box"><a href="quiz-04.html" class="internal"><span class="title">Quiz 4</span></a></div></li>
 </ul>
 </li>
 <li class="toc-item toc-chapter">