X-Git-Url: https://code.communitydata.science/stats_class_2020.git/blobdiff_plain/efa6913590499d105277c2907cde2a96aa7bd51f..f588b148aef8c3e05f61d1c0c245a0c4bede1693:/os_exercises/ch5_exercises_solutions.html diff --git a/os_exercises/ch5_exercises_solutions.html b/os_exercises/ch5_exercises_solutions.html index ef20494..a30a272 100644 --- a/os_exercises/ch5_exercises_solutions.html +++ b/os_exercises/ch5_exercises_solutions.html @@ -1569,15 +1569,15 @@ SE = \sqrt{\frac{p(1-p)}{n}}\\ \end{array}\]</span></p></li> </ol> </div> -<div id="twitter-users-and-news-part-i" class="section level1"> -<h1>5.8 Twitter users and news, Part I</h1> +<div id="twitter-users-news-i" class="section level1"> +<h1>5.8 Twitter users & news I</h1> <p>The general formula for a confidence interval is <span class="math inline">\(point~estimate~±~z^*\times~SE\)</span>. Where <span class="math inline">\(z^*\)</span> corresponds to the z-score for the desired value of <span class="math inline">\(\alpha\)</span>.</p> <p>To estimate the interval from the data described in the question, identify the three different values. The point estimate is 45%, <span class="math inline">\(z^* = 2.58\)</span> for a 99% confidence level (thatâs the number of standard deviations around the mean that ensure that 99% of a Z-score distribution is included), and <span class="math inline">\(SE = 2.4\%\)</span>. With this we can plug and chug:</p> <p><span class="math display">\[52\% ± 2.58 \times 2.4\%\]</span> And that yields: <span class="math display">\[95\% CI = (45.8\%, 58.2\%)\]</span></p> <p>Which means that from this data we are 99% confident that between 45.8% and 58.2% U.S. adult Twitter users get some news through the site.</p> </div> -<div id="twitter-users-and-news-part-ii" class="section level1"> -<h1>5.10 Twitter users and news, Part II</h1> +<div id="twitter-users-news-ii" class="section level1"> +<h1>5.10 Twitter users & news II</h1> <ol style="list-style-type: lower-alpha"> <li><p>False. See the answer to exercise 5.8 above. With <span class="math inline">\(\alpha = 0.01\)</span>, we can consult the 99% confidence interval. It includes 50% but also goes lower. A null hypothesis of <span class="math inline">\(p=0.50\)</span> would not be rejected at this level.</p></li> <li><p>False. The standard error of the sample proportion does not contain any information about the proportion of the population included in the sample. It estimates the variability of the sample proportion.</p></li>