Format

problemsetfinal/problemsetfinal.html

@@ -7,7 +7,7 @@
 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
 <meta name="author" content="Xiuyu Cao">
-<meta name="dcterms.date" content="2024-04-25">
+<meta name="dcterms.date" content="2024-04-26">
 
 <title>Fnial Problem Set</title>
 <style>
@@ -3191,7 +3191,7 @@ <h1 class="title">Fnial Problem Set</h1>
     <div>
     <div class="quarto-title-meta-heading">Published</div>
     <div class="quarto-title-meta-contents">
-      <p class="date">April 25, 2024</p>
+      <p class="date">April 26, 2024</p>
     </div>
   </div>
 
@@ -3317,8 +3317,8 @@ <h2 data-number="1.3" class="anchored" data-anchor-id="c"><span class="header-se
 <li>Continuous response data - Met.</li>
 <li>Sample is randomly selected from the population - Assume so.</li>
 <li>Observations are independent - Assume so.</li>
-<li>Equal variance between 2 groups - From the output of <code>var.test()</code>, <span class="math inline">\(P=0.69&gt;\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0: Equal variance.\)</span> Therefore, the assumption is met.</li>
-<li>Values are nearly normal or the sample size is large enough - From the outputs of the two Shapiro-Wilk tests, the P values are both greater than <span class="math inline">\(\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0: Normality.\)</span> of both groups. Therefore, the assumption of normal distribution is met.</li>
+<li>Equal variance between 2 groups - From the output of <code>var.test()</code>, <span class="math inline">\(P=0.69&gt;\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0:\)</span> <em>Equal variance.</em> Therefore, the assumption is met.</li>
+<li>Values are nearly normal or the sample size is large enough - From the outputs of the two Shapiro-Wilk tests, the P values are both greater than <span class="math inline">\(\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0:\)</span> <em>Normality</em> of both groups. Therefore, the assumption of normal distribution is met.</li>
 </ul>
 </section>
 <section id="d" class="level2" data-number="1.4">
@@ -3453,8 +3453,8 @@ <h2 data-number="2.3" class="anchored" data-anchor-id="c-1"><span class="header-
 <ul>
 <li>Continuous response data - Met.</li>
 <li>Samples must be independent - Assume so.</li>
-<li>Each population must have the same variance - From the output of the <code>leveneTest()</code>, <span class="math inline">\(P=0.73&gt;\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0: Equal variance.\)</span> Therefore, the assumption is met.</li>
-<li>The population of interest must be normally distributed - From the outputs of the Shapiro-Wilk tests, the P values are all greater than <span class="math inline">\(\alpha=0.05.\)</span> We thus fail to reject <span class="math inline">\(H_0: Normally distributed.\)</span> Therefore, the assumption is met.</li>
+<li>Each population must have the same variance - From the output of the <code>leveneTest()</code>, <span class="math inline">\(P=0.73&gt;\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0:\)</span> <em>Equal variance.</em> Therefore, the assumption is met.</li>
+<li>The population of interest must be normally distributed - From the outputs of the Shapiro-Wilk tests, the P values are all greater than <span class="math inline">\(\alpha=0.05.\)</span> We thus fail to reject <span class="math inline">\(H_0:\)</span> <em>Normally distributed.</em> Therefore, the assumption is met.</li>
 </ul>
 </section>
 <section id="d-1" class="level2" data-number="2.4">
@@ -3650,8 +3650,8 @@ <h2 data-number="4.3" class="anchored" data-anchor-id="c-3"><span class="header-
 <ul>
 <li>There is a linear relationship between the variables - From the plots, met.</li>
 <li>Statistical independence of the errors - Assume so.</li>
-<li>Homoscedasticity - <span class="math inline">\(P=0.95&gt;\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0: Homoscedasticity\)</span>. Therefore, the assumption is met.</li>
-<li>Residual normality - <span class="math inline">\(P=0.72&gt;\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0: Residual normality\)</span>. Therefore, the assumption is met.</li>
+<li>Homoscedasticity - <span class="math inline">\(P=0.95&gt;\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0:\)</span> <em>Homoscedasticity</em>. Therefore, the assumption is met.</li>
+<li>Residual normality - <span class="math inline">\(P=0.72&gt;\alpha=0.05\)</span>. We thus fail to reject <span class="math inline">\(H_0:\)</span> <em>Residual normality</em>. Therefore, the assumption is met.</li>
 </ul>
 </section>
 <section id="d-3" class="level2" data-number="4.4">

problemsetfinal/problemsetfinal.qmd

@@ -79,8 +79,8 @@ shapiro.test(wo_c$scores)
 * Continuous response data - Met.
 * Sample is randomly selected from the population - Assume so.
 * Observations are independent - Assume so.
-* Equal variance between 2 groups - From the output of `var.test()`, $P=0.69>\alpha=0.05$. We thus fail to reject $H_0: Equal variance.$ Therefore, the assumption is met.
-* Values are nearly normal or the sample size is large enough - From the outputs of the two Shapiro-Wilk tests, the P values are both greater than $\alpha=0.05$. We thus fail to reject $H_0: Normality.$ of both groups. Therefore, the assumption of normal distribution is met.
+* Equal variance between 2 groups - From the output of `var.test()`, $P=0.69>\alpha=0.05$. We thus fail to reject $H_0:$ *Equal variance.* Therefore, the assumption is met.
+* Values are nearly normal or the sample size is large enough - From the outputs of the two Shapiro-Wilk tests, the P values are both greater than $\alpha=0.05$. We thus fail to reject $H_0:$ *Normality* of both groups. Therefore, the assumption of normal distribution is met.
 
 
 ## d 
@@ -149,8 +149,8 @@ shapiro.test(drink3$scores)
 
 * Continuous response data - Met.
 * Samples must be independent - Assume so.
-* Each population must have the same variance - From the output of the `leveneTest()`, $P=0.73>\alpha=0.05$. We thus fail to reject $H_0: Equal variance.$ Therefore, the assumption is met.
-* The population of interest must be normally distributed - From the outputs of the Shapiro-Wilk tests, the P values are all greater than $\alpha=0.05.$ We thus fail to reject $H_0: Normally distributed.$ Therefore, the assumption is met.
+* Each population must have the same variance - From the output of the `leveneTest()`, $P=0.73>\alpha=0.05$. We thus fail to reject $H_0:$ *Equal variance.* Therefore, the assumption is met.
+* The population of interest must be normally distributed - From the outputs of the Shapiro-Wilk tests, the P values are all greater than $\alpha=0.05.$ We thus fail to reject $H_0:$ *Normally distributed.* Therefore, the assumption is met.
 
 
 ## d 
@@ -268,8 +268,8 @@ shapiro.test(residuals(lm.full))
 
 * There is a linear relationship between the variables - From the plots, met.
 * Statistical independence of the errors - Assume so.
-* Homoscedasticity - $P=0.95>\alpha=0.05$. We thus fail to reject $H_0: Homoscedasticity$. Therefore, the assumption is met.
-* Residual normality - $P=0.72>\alpha=0.05$. We thus fail to reject $H_0: Residual normality$. Therefore, the assumption is met.
+* Homoscedasticity - $P=0.95>\alpha=0.05$. We thus fail to reject $H_0:$ *Homoscedasticity*. Therefore, the assumption is met.
+* Residual normality - $P=0.72>\alpha=0.05$. We thus fail to reject $H_0:$ *Residual normality*. Therefore, the assumption is met.
 
 
 ## d