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docs: update education/statistics/2

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2026-02-11 14:19:33 +00:00
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title: 2 title: 2
description: description:
published: true published: true
date: 2026-02-11T14:17:36.454Z date: 2026-02-11T14:19:33.262Z
tags: tags:
editor: ckeditor editor: ckeditor
dateCreated: 2026-02-11T14:03:50.863Z dateCreated: 2026-02-11T14:03:50.863Z
@@ -28,7 +28,7 @@ dateCreated: 2026-02-11T14:03:50.863Z
<tbody> <tbody>
<tr> <tr>
<td style="padding:0mm 5.4pt;vertical-align:top;width:200px;"> <td style="padding:0mm 5.4pt;vertical-align:top;width:200px;">
<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Situation</strong></span></p> <p><span style="font-family:Arial, Helvetica, sans-serif;">Situation</span></p>
</td> </td>
<td style="padding:0mm 5.4pt;vertical-align:top;width:200px;"><span style="font-family:Arial, Helvetica, sans-serif;">n ≥ 30</span></td> <td style="padding:0mm 5.4pt;vertical-align:top;width:200px;"><span style="font-family:Arial, Helvetica, sans-serif;">n ≥ 30</span></td>
<td style="padding:0mm 5.4pt;vertical-align:top;width:200px;"><span style="font-family:Arial, Helvetica, sans-serif;">n &lt; 30</span><br><span style="font-family:Arial, Helvetica, sans-serif;">σ known</span></td> <td style="padding:0mm 5.4pt;vertical-align:top;width:200px;"><span style="font-family:Arial, Helvetica, sans-serif;">n &lt; 30</span><br><span style="font-family:Arial, Helvetica, sans-serif;">σ known</span></td>
@@ -101,5 +101,31 @@ dateCreated: 2026-02-11T14:03:50.863Z
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Level of Significance</span></h3> <h3><span style="font-family:Arial, Helvetica, sans-serif;">Level of Significance</span></h3>
<p><span style="font-family:Arial, Helvetica, sans-serif;">The maximum probability of committing a type I error, thus&nbsp;α<i> </i>is the rejection region.</span></p> <p><span style="font-family:Arial, Helvetica, sans-serif;">The maximum probability of committing a type I error, thus&nbsp;α<i> </i>is the rejection region.</span></p>
<p>&nbsp;</p> <p>&nbsp;</p>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Interval Estimate</span></h3> <h3><span style="font-family:Arial, Helvetica, sans-serif;">Critical Value (CV)</span></h3>
<p><span style="font-family:Arial, Helvetica, sans-serif;">An interval or a range of values used to estimate the parameter.</span></p> <p><span style="font-family:Arial, Helvetica, sans-serif;">The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.</span></p>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Compare CV with the test statistics:</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">P-value</span></h3>
<p><span style="font-family:Arial, Helvetica, sans-serif;">The probability value is the actual area under the standard distribution curve, representing the probability of a particular sample statistic, or if the statistic occurring if the null hypothesis is true.</span></p>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">If&nbsp;p &lt; α, reject the null hypothesis.</span></p>
<p>&nbsp;</p>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Procedure</span></h3>
<p><span style="font-family:Arial, Helvetica, sans-serif;">State the hypotheses and identify the claim.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Set&nbsp;H0 and H1.</span></p>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Check assumptions and conditions.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Independence and normality.</span></p>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Find the critical values and rejection region.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">One-sided or two-sided rejection region</span></p>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Compute the test value.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Z test or t test</span></p>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Decide whether the null hypothesis is rejected or not and draw the conclusion.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">H0 is rejected or not.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">There is (in)sufficient evidence that ...</span></p>
<p>&nbsp;</p>