ci exercises

book/_build/html/_sources/confidenceintervals.md

@@ -80,3 +80,33 @@ name: bernoulliCLT2wCI
 Each miniature histogram reflects $n=400$ coin flips where $p=0.2$. Grayed out histograms are those where the confidence interval misses the true parameter.
 ```
 
+## The Accuracy of Averages
+
+Proportions are a special kind of average. The sample average $\bar{x}$ estimates the  population average $\mu$. For general averages, there is no formula analogous to SD=$\sqrt{p(1-p)}$. The standard deviation must be estimated from the data. With a large simple random sample, the SD of the sample is a good estimate of the SD of the box. Then, the SE for the average can be calculated
+
+$$\text{SE for average} = \frac{\text{SD}}{\sqrt{n}}.$$
+
+Once the SE is found, a confidence interval is constructed like in the case of proportions. For example, a 95% confidence interval is $\bar{x} \pm 2\text{SE}$.
+
+## Exercises
+
+```{exercise-start}
+:label: CIicecream
+```
+In a survey of 96 randomly selected Americans, $\hat{p} = 0.60$ said they think ice cream should be banned. Find the 95% confidence interval for the proportion. 
+```{exercise-end}
+```
+
+```{exercise-start}
+:label: CInarrow
+```
+You are interested in the 95% confidence interval of a sample mean. Which of the following makes this interval more narrow?
+
+1. More observations.
+2. Fewer observations.
+3. Higher value of the average.
+4. Lower value of the average. 
+5. Both 1 and 4
+```{exercise-end}
+```
+

book/_build/html/confidenceintervals.html

@@ -427,6 +427,8 @@ <h2> Contents </h2>
 </li>
 </ul>
 </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-accuracy-of-averages">The Accuracy of Averages</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercises">Exercises</a></li>
 </ul>
             </nav>
         </div>
@@ -502,6 +504,37 @@ <h4>Interpretation of a Confidence Interval<a class="headerlink" href="#interpre
 </section>
 </section>
 </section>
+<section id="the-accuracy-of-averages">
+<h2>The Accuracy of Averages<a class="headerlink" href="#the-accuracy-of-averages" title="Permalink to this heading">#</a></h2>
+<p>Proportions are a special kind of average. The sample average <span class="math notranslate nohighlight">\(\bar{x}\)</span> estimates the  population average <span class="math notranslate nohighlight">\(\mu\)</span>. For general averages, there is no formula analogous to SD=<span class="math notranslate nohighlight">\(\sqrt{p(1-p)}\)</span>. The standard deviation must be estimated from the data. With a large simple random sample, the SD of the sample is a good estimate of the SD of the box. Then, the SE for the average can be calculated</p>
+<div class="math notranslate nohighlight">
+\[\text{SE for average} = \frac{\text{SD}}{\sqrt{n}}.\]</div>
+<p>Once the SE is found, a confidence interval is constructed like in the case of proportions. For example, a 95% confidence interval is <span class="math notranslate nohighlight">\(\bar{x} \pm 2\text{SE}\)</span>.</p>
+</section>
+<section id="exercises">
+<h2>Exercises<a class="headerlink" href="#exercises" title="Permalink to this heading">#</a></h2>
+<div class="exercise admonition" id="CIicecream">
+
+<p class="admonition-title"><span class="caption-number">Exercise 40 </span></p>
+<section id="exercise-content">
+<p>In a survey of 96 randomly selected Americans, <span class="math notranslate nohighlight">\(\hat{p} = 0.60\)</span> said they think ice cream should be banned. Find the 95% confidence interval for the proportion.</p>
+</section>
+</div>
+<div class="exercise admonition" id="CInarrow">
+
+<p class="admonition-title"><span class="caption-number">Exercise 41 </span></p>
+<section id="exercise-content">
+<p>You are interested in the 95% confidence interval of a sample mean. Which of the following makes this interval more narrow?</p>
+<ol class="arabic simple">
+<li><p>More observations.</p></li>
+<li><p>Fewer observations.</p></li>
+<li><p>Higher value of the average.</p></li>
+<li><p>Lower value of the average.</p></li>
+<li><p>Both 1 and 4</p></li>
+</ol>
+</section>
+</div>
+</section>
 </section>
 
     <script type="text/x-thebe-config">
@@ -574,6 +607,8 @@ <h4>Interpretation of a Confidence Interval<a class="headerlink" href="#interpre
 </li>
 </ul>
 </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-accuracy-of-averages">The Accuracy of Averages</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercises">Exercises</a></li>
 </ul>
   </nav></div>
 

book/confidenceintervals.md

@@ -90,4 +90,30 @@ Once the SE is found, a confidence interval is constructed like in the case of p
 
 ## Exercises
 
-TK
+```{exercise-start}
+:label: CIicecream
+```
+In a survey of 96 randomly selected Americans, $\hat{p} = 0.60$ said they think ice cream should be banned. Find the 95% confidence interval for the proportion. 
+```{exercise-end}
+```
+
+```{exercise-start}
+:label: CInarrow
+```
+You are interested in the 95% confidence interval of a sample mean. Which of the following makes this interval more narrow?
+
+1. More observations.
+2. Fewer observations.
+3. Higher value of the average.
+4. Lower value of the average. 
+5. Both 1 and 4
+```{exercise-end}
+```
+
+```{exercise-start}
+:label: CImc
+```
+Consider a multiple choice exam with choices A, B, C, D, and E for each question. Assume that the probability that a particular question has the answer $C$ is $p = 0.2$ and that all letter answers are determined independently. Find a 90% confidence interval for the proportion of questions that will have a correct answer of C on a 1600-question exam. 
+```{exercise-end}
+```
+