Latest build deployed.

.devcontainer/devcontainer.json

@@ -1,86 +0,0 @@
-// This file was automatically generated with PreTeXt 2.34.0.
-// If you modify this file, PreTeXt will no longer automatically update it.
-//
-//////////////////////////////////////////////////////////////
-//
-// This file provides configuration options so that a PreTeXt
-//   project can be edited and built using GitHub's Codespaces.
-// It is recommended to keep this in your repository even if you
-//   do not use this feature, as it will allow other to explore
-//   your project easily.
-// This file will be automatically generated by PreTeXt with the
-//   latest updates unless you remove the first comment line above.
-//
-///////////////////////////////////////////////////////////////
-{
-  "image": "pretextbook/pretext-full:1.6", // uses latest image from https://hub.docker.com/r/PreTeXtBook/pretext-full/tags
-  // If you don't need sagemath, you can use a smaller base image.  Comment out the line above and uncomment the line below to use a smaller image.
-  // "image": "pretextbook/pretext:1.6",
-  "features": {"ghcr.io/devcontainers/features/github-cli": {}},
-
-  // The pretext-full image above includes pretext, prefigure, and enough parts of latex and sagemath for most cases.  Here we install additional dependencies.
-  "postCreateCommand": {
-    "install pandoc": "bash ./.devcontainer/installPandoc.sh",
-    "mark repo as safe": "git config --global --add safe.directory $(pwd)"
-    },
-
-
-  // Port forwarding
-  // ---------------
-  // This is needed by the CodeChat Server.
-  "forwardPorts": [
-    // The port used for a Thrift connection between the VSCode CodeChat
-    // extension and the CodeChat Server.
-    27376,
-    // The port used for an HTTP connection from the CodeChat Client to
-    // the CodeChat Server.
-    27377,
-    // The port used by a websocket connection between the CodeChat
-    // Server and the CodeChat Client.
-    27378
-  ],
-  // See the [docs](https://containers.dev/implementors/json_reference/#port-attributes).
-  "portsAttributes": {
-    "27376": {
-      "label": "VSCode extension <-> CodeChat Server",
-      "requireLocalPort": true
-    },
-    "27377": {
-      "label": "CodeChat Client",
-      "requireLocalPort": true
-    },
-    "27378": {
-      "label": "CodeChat Client<->Server websocket",
-      "requireLocalPort": true
-      // This port needs to be public; however, there's no way to specify port visibility here. See `server.py` in the CodeChat Server for details.
-    }
-  },
-
-
-  // Configure tool-specific properties.
-  "customizations": {
-    "codespaces": {
-      "openFiles": ["README.md"]
-    },
-    "vscode": {
-      "settings": {
-        "editor.quickSuggestions": {
-          "other": "off"
-        },
-        "editor.suggest.showProperties": false,
-        "editor.snippetSuggestions": "bottom",
-        "files.autoSave": "afterDelay",
-        "xml.validation.enabled": true,
-        "redhat.telemetry.enabled": false,
-        "CodeChat.CodeChatServer.Command": "CodeChat_Server"
-      },
-      "extensions": [
-        "oscarlevin.pretext-tools",
-        "CodeChat.codechat",
-        "streetsidesoftware.code-spell-checker",
-        "alpinebuster.vscode-latex-table-editor",
-        "mathematic.vscode-pdf"
-      ]
-    }
-  }
-}

.devcontainer/installLatex.sh

@@ -1,29 +0,0 @@
-#!/usr/bin/env bash
-
-# This file was automatically generated with PreTeXt 2.19.3.
-# If you modify this file, PreTeXt will no longer automatically update it.
-
-# We use TinyTeX (https://yihui.org/tinytex/)
-wget -qO- "https://yihui.org/tinytex/install-bin-unix.sh" | sh
-
-tlmgr install adjustbox amscdx bold-extra braket bussproofs cancel carlisle cases chessfss circuitikz colortbl enumitem extpfeil fontawesome5 fontaxes gensymb imakeidx jknapltx kastrup lambda-lists listings listingsutf8 makeindex marvosym mathalpha mathtools menukeys mhchem microtype musicography newpx newtx nicematrix pdfcol pdfpages pdflscape pgfplots phaistos physics polyglossia pstricks realscripts relsize siunitx skak skaknew smartdiagram snapshot stmaryrd tcolorbox tikz-cd tikzfill titlesec txfonts ulem upquote was xfrac xltxtra xpatch xstring 
-
-tlmgr path add
-
-#  Ensure fonts provided by TinyTeX are available, as suggested in the pretext guide
-fontconfig="<?xml version=\"1.0\"?>
-<!DOCTYPE fontconfig SYSTEM \"fonts.dtd\">
-<fontconfig>
-  <dir>~/.TinyTeX/texmf-dist/fonts</dir>
-  <dir>~/.TinyTeX/texmf-local/fonts</dir>
-</fontconfig>"
-
-fontconfig_path="/etc/fonts/conf.d/09-texlive-fonts.conf"
-if [ ! -f "$fontconfig_path" ]; then
-    echo "Creating fontconfig file at $fontconfig_path"
-    echo "$fontconfig" | sudo tee "$fontconfig_path" > /dev/null
-else
-    echo "Fontconfig file already exists at $fontconfig_path"
-fi
-# Update font cache
-fc-cache -f -v

.devcontainer/installPandoc.sh

@@ -1,17 +0,0 @@
-#!/usr/bin/env bash
-
-# This file was automatically generated with PreTeXt 2.34.0.
-# If you modify this file, PreTeXt will no longer automatically update it.
-
-wget https://github.com/jgm/pandoc/releases/download/3.8.3/pandoc-3.8.3-1-amd64.deb -O pandoc.deb
-
-# wait for 60 second and then double check that no other script is using apt-get:
-sleep 60
-while fuser /var/lib/dpkg/lock >/dev/null 2>&1; do
-    echo "Waiting for apt-get to be free..."
-    sleep 15
-done
-# Install pandoc
-apt-get install -y --no-install-recommends ./pandoc.deb 
-
-rm pandoc.deb

.devcontainer/installPretext.sh

@@ -1,29 +0,0 @@
-#!/usr/bin/env bash
-
-# This file was automatically generated with PreTeXt 2.19.3.
-# If you modify this file, PreTeXt will no longer automatically update it.
-
-sudo apt-get update 
-sudo apt-get install -y --no-install-recommends \
-                    python3-louis \
-                    libcairo2-dev \
-                    librsvg2-bin
-
-pip install --upgrade pip --break-system-packages
-
-pip install pretext[homepage,prefigure] pycairo --only-binary {greenlet}  --break-system-packages
-
-pip install codechat-server --break-system-packages
-
-playwright install-deps
-
-playwright install
-
-
-# echo '/usr/lib/python3/dist-packages' > /usr/local/lib/python3.8/dist-packages/louis.pth
-prefig init
-
-# Install mermaid for diagrams
-npm install -g @mermaid-js/mermaid-cli
-
-echo "PreTeXt installation complete."

.devcontainer/installSage.sh

@@ -1,21 +0,0 @@
-#!/usr/bin/env bash
-
-# This file was automatically generated with PreTeXt 2.33.2.
-# If you modify this file, PreTeXt will no longer automatically update it.
-
-# Conda should already be installed in the codespace.  We need to add the conda-forge channel
-
-conda config --add channels conda-forge
-conda config --set channel_priority strict
-
-# We don't want conda to open the base environment always:
-conda config --set auto_activate_base false
-
-# Now create a conda environment for sage (called sage):
-conda create --yes -n sage sage python=3.12
-
-conda init
-
-echo 'conda activate sage' >> ~/.bashrc
-
-source ~/.bashrc

.github/workflows/pretext-cli.yml

@@ -1,117 +0,0 @@
-# This file was automatically generated with PreTeXt 2.33.2.
-# If you modify this file, PreTeXt will no longer automatically update it.
-#
-# This workflow file can be used to automatically build a project and create
-# an artifact for deployment.  It can also be used to deploy the project to
-# GitHub Pages or Cloudflare Pages.
-#
-# The workflow is triggered on pull requests or can be run manually.  You can uncomment
-# the `push` event to have it run on pushes to the main branch as well.
-name: PreTeXt-CLI Actions
-on:
-    # Runs on pull requests
-    pull_request:
-        branches: ["*"]
-    ## Runs on pushes to main
-    #push:
-    #    branches: ["main"]
-    # Runs on demand
-    workflow_dispatch:
-
-jobs:
-    build:
-        runs-on: ubuntu-latest
-        container: oscarlevin/pretext-full
-
-        steps:
-            - name: Checkout source
-              uses: actions/checkout@v4
-
-            - name: install deps
-              run: pip install -r requirements.txt
-
-            - name: set up node
-              uses: actions/setup-node@v4
-              with:
-                node-version: '22'
-
-            - name: install local ptx files
-              run: pretext --version
-
-            - name: build deploy targets
-              run: |
-                version="$(pretext --version)"
-                major="$(echo $version | cut -d '.' -f 1)"
-                minor="$(echo $version | cut -d '.' -f 2)"
-                if [ "$major" -ge 2 -a "$minor" -ge 5 ]; then
-                    echo "PreTeXt version is 2.5 or greater; using new build command"
-                    pretext build --deploys
-                else
-                    echo "PreTeXt version is less than 2.5, using old build command"
-                    pretext build
-                fi
-            - name: stage deployment
-              run: pretext deploy --stage-only
-
-            - name: Bundle output/stage as artifact
-              uses: actions/upload-artifact@v4
-              with:
-                  name: deploy
-                  path: output/stage
-
-    deploy-cloudflare:
-        runs-on: ubuntu-latest
-        needs: build
-        if: vars.CLOUDFLARE_PROJECT_NAME != ''
-        permissions:
-          contents: read
-          deployments: write
-
-        steps:
-            - name: Download artifact
-              uses: actions/download-artifact@v4
-              with:
-                  name: deploy
-                  path: deploy
-            - name: Create 404.html
-              run: echo "404 page not found" >> deploy/404.html
-            - name: Publish to Cloudflare
-              uses: cloudflare/pages-action@v1
-              with:
-                  apiToken: ${{ secrets.CLOUDFLARE_API_TOKEN }}
-                  accountId: ${{ secrets.CLOUDFLARE_ACCOUNT_ID }}
-                  projectName: ${{ vars.CLOUDFLARE_PROJECT_NAME }}
-                  gitHubToken: ${{ secrets.GITHUB_TOKEN }}
-                  branch:  ${{ github.head_ref || github.ref_name }}
-                  directory: deploy
-
-    deploy-ghpages:
-        runs-on: ubuntu-latest
-        needs: build
-        if: vars.PTX_ENABLE_DEPLOY_GHPAGES == 'yes' && github.ref == format('refs/heads/{0}', github.event.repository.default_branch)
-        permissions:
-            contents: read
-            pages: write
-            id-token: write
-        concurrency:
-            group: "page"
-            cancel-in-progress: false
-        environment:
-            name: github-pages
-            url: ${{ steps.deployment.outputs.page_url }}
-        steps:
-            - name: Download website artifact
-              uses: actions/download-artifact@v4
-              with:
-                  name: deploy
-                  path: deploy
-            - name: Setup GitHub Pages
-              id: check
-              uses: actions/configure-pages@v4
-            - name: Upload artifact
-              uses: actions/upload-pages-artifact@v3
-              with:
-                  path: deploy
-            - name: Deploy to Github Pages
-              id: deployment
-              uses: actions/deploy-pages@v4

.github/workflows/pretext-deploy.yml

@@ -1,68 +0,0 @@
-# This file was automatically generated with PreTeXt 2.33.2.
-# If you modify this file, PreTeXt will no longer automatically update it.
-#
-
-name: Build and Deploy
-on:
-  # Currently, this workflow only runs when manually selected (the `workflow_dispatch` event).
-  # If you would like it to run on other events, uncomment some of the lines below.
-
-  # # Runs on pull requests
-  # pull_request:
-  #     branches: ["*"]
-
-  # # Runs on pushes to main
-  # push:
-  #     branches: ["main"]
-
-  # # Runs every day at 00:00 UTC
-  # schedule:
-  #     - cron: '0 0 * * *'
-
-  # Runs on demand
-  workflow_dispatch:
-
-permissions:
-  contents: write
-
-jobs:
-  build-and-deploy:
-    runs-on: ubuntu-latest
-    container: oscarlevin/pretext-full
-
-    steps:
-      - name: Checkout source
-        uses: actions/checkout@v4
-
-      - name: set up node
-        uses: actions/setup-node@v4
-        with:
-          node-version: '22'
-
-      - name: add gh-cli
-        run: |
-          apt-get update
-          apt-get install gh jq -y
-
-      - name: setup git config
-        run: |
-          git config --global --add safe.directory $(pwd)
-          git config user.name "${{ github.actor }} via GitHub Actions"
-          git config user.email "${{ github.actor }}@github_actions.no_reply"
-
-      - name: install deps
-        run: pip install -r requirements.txt --break-system-packages
-
-      - name: install local ptx files
-        run: pretext --version
-
-      - name: build deploy targets
-        run: pretext build --deploys
-
-      - name: run deploy
-        run: pretext deploy --no-push
-
-      - name: push gh-pages branch
-        run: git push origin gh-pages --force
-        env:
-          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}

.gitignore

@@ -1,107 +0,0 @@
-# This file was automatically generated with PreTeXt 2.34.0.
-# If you modify this file, PreTeXt will no longer automatically update it.
-#
-# Boilerplate list of files in a PreTeXt project for git to ignore
-# ensure this file is tracked
-!.gitignore
-
-# don't track unpublished builds or stage (note: Runestone uses `published`)
-output
-published
-
-# don't track assets generated from source
-generated-assets
-.cache
-
-# don't track the executables.ptx file
-executables.ptx
-
-# don't track node packages
-node_modules
-
-# don't track error logs
-.error_schema.log
-logs
-
-# don't track OS related files (windows/macos/linux)
-.DS_Store
-.DS_Store?
-._*
-.AppleDouble
-.LSOverride
-.Spotlight-V100
-.Trashes
-Icon
-.AppleDB
-.AppleDesktop
-Network Trash Folder
-Temporary Items
-.apdisk
-Thumbs.db
-Thumbs.db:encryptable
-ehthumbs.db
-ehthumbs_vista.db
-*.stackdump
-*.lnk
-*.cab
-*.msi
-*.msix
-*.msm
-*.msp
-[Dd]esktop.ini
-.directory
-.fuse_hidden*
-.Trash-*
-.nfs*
-
-# Don't include VSCode generated files
-.vscode
-*.code-workspace
-
-# Don't inlucde SublimeText files
-# Cache files for Sublime Text
-*.tmlanguage.cache
-*.tmPreferences.cache
-*.stTheme.cache
-
-# Workspace files are user-specific
-*.sublime-workspace
-
-# Project files should be checked into the repository, unless a significant
-# proportion of contributors will probably not be using Sublime Text
-*.sublime-project
-
-# SFTP configuration file
-sftp-config.json
-sftp-config-alt*.json
-
-# Package control specific files
-Package Control.last-run
-Package Control.ca-list
-Package Control.ca-bundle
-Package Control.system-ca-bundle
-Package Control.cache/
-Package Control.ca-certs/
-Package Control.merged-ca-bundle
-Package Control.user-ca-bundle
-oscrypto-ca-bundle.crt
-bh_unicode_properties.cache
-
-# Sublime-github package stores a github token in this file
-# https://packagecontrol.io/packages/sublime-github
-GitHub.sublime-settings
-
-# Don't track common virtual environment directories
-venv/
-
-# Don't include Dropbox settings and caches
-.dropbox
-.dropbox.attr
-.dropbox.cache
-
-# Don't track codechat config (will be generated automatically)
-codechat_config.yaml
-
-# Don't track deprecated workflows
-.github/workflows/deploy.yml
-.github/workflows/test-build.yml

LICENSE

@@ -1,21 +0,0 @@
-MIT License
-
-Copyright (c) 2025 Oscar Levin
-
-Permission is hereby granted, free of charge, to any person obtaining a copy
-of this software and associated documentation files (the "Software"), to deal
-in the Software without restriction, including without limitation the rights
-to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the Software is
-furnished to do so, subject to the following conditions:
-
-The above copyright notice and this permission notice shall be included in all
-copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-SOFTWARE.

README.md

@@ -1,3 +0,0 @@
-# Fall 2026 Math 1044
-
-Course materials produced using PreTeXt.

archives.html

@@ -0,0 +1,31 @@
+<!DOCTYPE html>
+<html lang="en">
+  <head>
+      <title>Introduction to Probability and Statistics for the Life Sciences - Archives</title>
+      <meta charset="utf-8" />
+      <meta name="generator" content="Pelican" />
+      <meta name="viewport" content="width=device-width, initial-scale=1.0">
+      <link rel="stylesheet" type="text/css" href="./theme/css/style.css" />
+        <meta name="description" content="Spring 2026 MATH 1044" />
+  </head>
+
+  <body>
+    <header>
+      <nav>
+        <a href="/">Home</a>
+      </nav>
+      <h1>Introduction to Probability and Statistics for the Life Sciences</h1>
+<p>Spring 2026 MATH 1044</p>    </header>
+    <main>
+    <h2>Archives for Introduction to Probability and Statistics for the Life Sciences</h2>
+
+    <dl>
+    </dl>
+    </main>
+    <footer>
+      <address>
+        Site generated by <a href="https://github.com/pretextbook/pretext-cli">PreTeXt-CLI</a>.
+      </address>
+    </footer>
+  </body>
+</html>

authors.html

@@ -0,0 +1,30 @@
+<!DOCTYPE html>
+<html lang="en">
+  <head>
+      <title>Introduction to Probability and Statistics for the Life Sciences - Authors</title>
+      <meta charset="utf-8" />
+      <meta name="generator" content="Pelican" />
+      <meta name="viewport" content="width=device-width, initial-scale=1.0">
+      <link rel="stylesheet" type="text/css" href="./theme/css/style.css" />
+        <meta name="description" content="Spring 2026 MATH 1044" />
+  </head>
+
+  <body>
+    <header>
+      <nav>
+        <a href="/">Home</a>
+      </nav>
+      <h1>Introduction to Probability and Statistics for the Life Sciences</h1>
+<p>Spring 2026 MATH 1044</p>    </header>
+    <main>
+    <h2>Authors on Introduction to Probability and Statistics for the Life Sciences</h2>
+    <ul>
+    </ul>
+    </main>
+    <footer>
+      <address>
+        Site generated by <a href="https://github.com/pretextbook/pretext-cli">PreTeXt-CLI</a>.
+      </address>
+    </footer>
+  </body>
+</html>

categories.html

@@ -0,0 +1,30 @@
+<!DOCTYPE html>
+<html lang="en">
+  <head>
+      <title>Introduction to Probability and Statistics for the Life Sciences - Categories</title>
+      <meta charset="utf-8" />
+      <meta name="generator" content="Pelican" />
+      <meta name="viewport" content="width=device-width, initial-scale=1.0">
+      <link rel="stylesheet" type="text/css" href="./theme/css/style.css" />
+        <meta name="description" content="Spring 2026 MATH 1044" />
+  </head>
+
+  <body>
+    <header>
+      <nav>
+        <a href="/">Home</a>
+      </nav>
+      <h1>Introduction to Probability and Statistics for the Life Sciences</h1>
+<p>Spring 2026 MATH 1044</p>    </header>
+    <main>
+    <h2>Categories on Introduction to Probability and Statistics for the Life Sciences</h2>
+    <ul>
+    </ul>
+    </main>
+    <footer>
+      <address>
+        Site generated by <a href="https://github.com/pretextbook/pretext-cli">PreTeXt-CLI</a>.
+      </address>
+    </footer>
+  </body>
+</html>

course/.mapping.json

@@ -0,0 +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/quizzes/quiz-04.ptx": ["quiz-04"], "source/quizzes/quiz-05.ptx": ["quiz-05"], "source/exams/exam-01.ptx": ["exam-01"], "source/exams/exam-02.ptx": ["exam-02"], "source/recitations/calculus-review.ptx": ["recitation-calculus-review"], "source/review/Exam-1-Review.ptx": ["Exam-1-Review"], "source/review/Exam-2-Review.ptx": ["Exam-2-Review"], "source/review/Final-Exam-Review.ptx": ["Final-Exam-Review"], "source/fun/boxes.ptx": ["boxes"]}

course/Exam-2-Review.html

@@ -0,0 +1,575 @@
+<!DOCTYPE html>
+<!--********************************************-->
+<!--*       Generated from PreTeXt source      *-->
+<!--*                                          *-->
+<!--*         https://pretextbook.org          *-->
+<!--*                                          *-->
+<!--********************************************-->
+<html lang="en-US" dir="ltr">
+<!--******************************************-->
+<!--*  Authored with PreTeXt                 *-->
+<!--*  pretextbook.org                       *-->
+<!--*  Theme: boulder                        *-->
+<!--*  Palette:                              *-->
+<!--******************************************-->
+<head xmlns:og="http://ogp.me/ns#" xmlns:book="https://ogp.me/ns/book#">
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+<title>Exam 2 Review</title>
+<link rel="preconnect" href="https://fonts.googleapis.com">
+<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin="">
+<link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=Material+Symbols+Outlined:opsz,wght,FILL,GRAD@24,400,0,0">
+<link href="_static/pretext/css/theme.css" rel="stylesheet" type="text/css">
+<script>
+var runestoneMathReady = new Promise((resolve) => window.rsMathReady = resolve);
+window.MathJax = {
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+      [
+        "\\(",
+        "\\)"
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+    ],
+    "tags": "none",
+    "tagSide": "right",
+    "tagIndent": ".8em",
+    "packages": {
+      "[+]": [
+        "base",
+        "extpfeil",
+        "ams",
+        "amscd",
+        "color",
+        "newcommand",
+        "knowl"
+      ]
+    }
+  },
+  "options": {
+    "ignoreHtmlClass": "tex2jax_ignore|ignore-math",
+    "processHtmlClass": "process-math"
+  },
+  "chtml": {
+    "scale": 0.98,
+    "mtextInheritFont": true
+  },
+  "loader": {
+    "load": [
+      "input/asciimath",
+      "[tex]/extpfeil",
+      "[tex]/amscd",
+      "[tex]/color",
+      "[tex]/newcommand",
+      "[pretext]/mathjaxknowl3.js"
+    ],
+    "paths": {
+      "pretext": "_static/pretext/js"
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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>
+<p class="byline">Andy Eisenberg</p>
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+<ul class="structural toc-item-list">
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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>
+<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>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-13.html#subsec-Probability" class="internal"><span class="title">Sec 1.2: Probability</span></a></div></li>
+</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>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-15.html#subsec-Diagnostic-Testing" class="internal"><span class="title">Diagnostic Testing</span></a></div></li>
+<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>
+</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>
+<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>
+</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">
+<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>
+<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>
+</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">
+<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>
+<li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-01-27.html#subsec-Joint-Distributions" class="internal"><span class="title">Joint Distributions</span></a></div></li>
+</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>
+</li>
+<li class="toc-item toc-section">
+<div class="toc-title-box"><a href="notes-02-03.html" class="internal"><span class="title">Tuesday, Feb 3</span></a></div>
+<ul class="structural toc-item-list"><li class="toc-item toc-subsection"><div class="toc-title-box"><a href="notes-02-03.html#notes-02-03-3" class="internal"><span class="title">Variance</span></a></div></li></ul>
+</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>
+<ul class="structural toc-item-list">
+<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>
+</ul>
+</li>
+</ul>
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+<div class="toc-title-box"><a href="quizzes.html" class="internal"><span class="title">Quizzes</span></a></div>
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+</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">
+<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>
+</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>
+</div></section><section class="subsection" id="Exam-2-Review-3"><h3 class="heading hide-type">
+<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>
+</div>
+<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">140<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 140: "><a href="#Exam-2-Review-4-6-1-2" title="Copy heading and permalink for Table 140: " aria-label="Copy heading and permalink for Table 140: ">🔗</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">141<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 141: "><a href="#Exam-2-Review-4-7-1-2" title="Copy heading and permalink for Table 141: " aria-label="Copy heading and permalink for Table 141: ">🔗</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">142<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 142: "><a href="#Exam-2-Review-4-19-1-2" title="Copy heading and permalink for Table 142: " aria-label="Copy heading and permalink for Table 142: ">🔗</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">143<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 143: "><a href="#Exam-2-Review-4-20-1-2" title="Copy heading and permalink for Table 143: " aria-label="Copy heading and permalink for Table 143: ">🔗</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>
+<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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