wiki/education/statistics/2.html

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<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>&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>&nbsp;</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>&nbsp;</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>&nbsp;</p>
<figure class="table">
  <table>
    <tbody>
      <tr>
        <td style="padding:0mm 5.4pt;vertical-align:top;width:100px;">
          <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>
      </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>&nbsp;</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>&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>&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>&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>