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_sources/confidenceintervals.md

@@ -84,7 +84,7 @@ Each miniature histogram reflects $n=400$ coin flips where $p=0.2$. Grayed out h
 
 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
 
-$$\text{SE for average} = \frac{\text{SD}}{n}.$$
+$$\text{SE for average} = \frac{\text{SD}}{\sqrt{n}}.$$
 
 Once the SE is found, a confidence interval is constructed like in the case of proportions. For example, a 95% confidence interval is $\bar{x} \pm 2\text{SE}$.
 

confidenceintervals.html

@@ -510,7 +510,7 @@ <h4>Interpretation of a Confidence Interval<a class="headerlink" href="#interpre
 <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">
-\[\text{SE for average} = \frac{\text{SD}}{n}.\]</div>
+\[\text{SE for average} = \frac{\text{SD}}{\sqrt{n}}.\]</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">