106 lines
13 KiB
HTML
106 lines
13 KiB
HTML
<!--
|
||
title: 2
|
||
description:
|
||
published: true
|
||
date: 2026-02-11T14:17:36.454Z
|
||
tags:
|
||
editor: ckeditor
|
||
dateCreated: 2026-02-11T14:03:50.863Z
|
||
-->
|
||
|
||
<h2><span style="font-family:Arial, Helvetica, sans-serif;">General</span></h2>
|
||
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Point Estimate</span></h3>
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">A specific numerical value estimate of a parameter. The best point estimate of the population mean μ is the sample mean x̄.</span></p>
|
||
<p> </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> </p>
|
||
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Confidence Interval (CI)</span></h3>
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">A range of values constructed from sample data so that parameter occurs within that range at a specified probability. The specified probability is called the level of confidence.</span></p>
|
||
<p> </p>
|
||
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Maximum error of estimate</span></h3>
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">The maximum likely difference between the point estimate of a parameter and the actual value of the parameter.</span></p>
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">Minimum sample size needed for an interval estimate of the population mean, when n ≥ 30.</span></p>
|
||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||
<p> </p>
|
||
<figure class="table">
|
||
<table>
|
||
<tbody>
|
||
<tr>
|
||
<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: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><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 < 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;">
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">Test</span></p>
|
||
</td>
|
||
<td style="padding:0mm 5.4pt;vertical-align:top;">
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">Z</span></p>
|
||
</td>
|
||
<td style="padding:0mm 5.4pt;vertical-align:top;">
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">Z</span></p>
|
||
</td>
|
||
<td style="padding:0mm 5.4pt;vertical-align:top;">
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">t</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td style="padding:0mm 5.4pt;vertical-align:top;"><span style="font-family:Arial, Helvetica, sans-serif;">CI</span></td>
|
||
<td style="padding:0mm 5.4pt;vertical-align:top;" colspan="2">
|
||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||
</td>
|
||
<td style="padding:0mm 5.4pt;vertical-align:top;">
|
||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</figure>
|
||
<p> </p>
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">When testing for = or ≠, α need to be divided by 2.</span></p>
|
||
<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> </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, H0 states that there are no differences in between.</span></p>
|
||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">Alternative hypothesis, H1 states that there are differences in between.</span></p>
|
||
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
||
<p> </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> </p>
|
||
<figure class="table">
|
||
<table>
|
||
<tbody>
|
||
<tr>
|
||
<td style="width:200px;"> </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> </p>
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">The probability of type I error is denoted by α<i>.</i></span></p>
|
||
<p><span style="font-family:Arial, Helvetica, sans-serif;">The probability of type II error is denoted by β.</span></p>
|
||
<p> </p>
|
||
<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 α<i> </i>is the rejection region.</span></p>
|
||
<p> </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>
|