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docs: update education/statistics/2

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2026-02-11 14:17:03 +00:00
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@@ -2,7 +2,7 @@
title: 2
description:
published: true
date: 2026-02-11T14:14:04.416Z
date: 2026-02-11T14:17:02.463Z
tags:
editor: ckeditor
dateCreated: 2026-02-11T14:03:50.863Z
@@ -27,12 +27,12 @@ dateCreated: 2026-02-11T14:03:50.863Z
<table>
<tbody>
<tr>
<td style="padding:0mm 5.4pt;vertical-align:top;width:100px;">
<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>
</td>
<td style="padding:0mm 5.4pt;vertical-align:top;width:100px;"><span style="font-family:Arial, Helvetica, sans-serif;">n ≥ 30</span></td>
<td style="padding:0mm 5.4pt;vertical-align:top;width:100px;"><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:100px;"><span style="font-family:Arial, Helvetica, sans-serif;">n &lt; 30</span><br><span style="font-family:Arial, Helvetica, sans-serif;">σ unknown</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 unknown</span></td>
</tr>
<tr>
<td style="padding:0mm 5.4pt;vertical-align:top;">
@@ -65,8 +65,38 @@ dateCreated: 2026-02-11T14:03:50.863Z
<p><span style="font-family:Arial, Helvetica, sans-serif;">Thus, Zα/2 are used. Otherwise, use Zα.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">If σ is unknown, replace by s.</span></p>
<p>&nbsp;</p>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Interval Estimate</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;">Testing Hypothesis is a statistical hypothesis, in which states if there are differences between a parameter and a specific value, or between two parameters.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Null hypothesis,&nbsp;H0 states that there are no differences in between.</span></p>
<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAAXCAMAAAC73rTSAAAAAXNSR0IArs4c6QAAAKhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZjoAZjo6ZmaQZpC2ZpDbZra2ZrbbZrb/kDoAkDpmkGYAkGY6kGZmkLbbkLb/kNv/tmYAtmY6tpA6tpBmtpCQtrZmttvbttv/tv//25A625Bm27Zm27aQ29vb29v/2////7Zm/9uQ/9u2/9vb//+2///b/7/JaAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACZklEQVRIS+2Vf3OaQBCGWazJ2WgKmKSGFlMh1FISWgG57//Nuj9OUMDITDu1nXH/8O7W4/Zl99nDsi52ycAlA/99BioXYPTdMsP5X2e7aWso3FGCvkqGc1gWOE3YV7h5OhRRKP67UNfnEKezeVsRembf9rTk8EirVIa/avqr18kXCdDxxJ7V9UyRQPT59qojrgwA4BahKOcA0/V0o2Nlr3QE9hfZy2t6O/pFP8A7qo+OFNgPJ951G0961cljZaDs+58cw8djya66dKrrjfax8jlOMMWOlS4KtVgmlWs20xoB0T6tQ4Q4o2WhrhL9md+bLTURaMC/d177Qyfi/jvpZ2GvcnnoQVBkhA5uoYmgUKgbavma10Khl9fijFZme9gI7E/lNlaDMngcwZpKmXAZBVXTV5wd8vIZNSTk+hENQRpZO82gIGiFguCLgplJvPZNDswk5LJyYvKGV/aK9tJjXpmZ93cD7yyddfrksIsFH0ORlY+Scle+uo5SYWGAkRSVbLzJnEEtw1d++77qZ7ApfDZnysRe1eE9aI7bhcedJqVNIBaoA4JNiisq2RjBdILrYmo4lRP1su6RJviQWftLkgIHk4Ebpq4fdaWOHNQzSvRyDY/ZrdCGEspPEj8HR8cffVyvYWHpZ6o1PVd6e0lp6epvnyNNlUvnm6FyMXwtsPLwWltQmjyYJbhCwuSYCMYGMR3AeMXrYq6A5pg8vD3Hrc/VvkYjpVX4ncA3eZAMnrofhhTqrT3SbW3r97Z2MVxp7/O/q6p5nsvUsX5vZ1uKtPnH6fkjKlOiphu519vZRp9Tusv+GfsF5BpCacTkX/kAAAAASUVORK5CYII="></figure>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Alternative hypothesis,&nbsp; H1&nbsp;states that there are differences in between.</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">A statistical test uses the data obtained from a sample to make the decision about the null hypothesis that should be rejected or not. The numerical value obtained from a statistical test is called the test value.</span></p>
<p>&nbsp;</p>
<figure class="table">
<table>
<tbody>
<tr>
<td style="width:200px;">&nbsp;</td>
<td style="width:200px;"><span style="font-family:Arial, Helvetica, sans-serif;">Accept H0</span></td>
<td style="width:200px;"><span style="font-family:Arial, Helvetica, sans-serif;">Reject H0</span></td>
</tr>
<tr>
<td><span style="font-family:Arial, Helvetica, sans-serif;">H0 is true</span></td>
<td><span style="font-family:Arial, Helvetica, sans-serif;">Correct</span></td>
<td><span style="font-family:Arial, Helvetica, sans-serif;">Type I Error</span></td>
</tr>
<tr>
<td><span style="font-family:Arial, Helvetica, sans-serif;">H0 is false</span></td>
<td><span style="font-family:Arial, Helvetica, sans-serif;">Type II Error</span></td>
<td><span style="font-family:Arial, Helvetica, sans-serif;">Correct</span></td>
</tr>
</tbody>
</table>
</figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">The probability of type I error is denoted by&nbsp;<i>α.</i></span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">The probability of type II error is denoted by&nbsp;β.</span></p>
<p>&nbsp;</p>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Interval Estimate</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>