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alexanderthclark committed Mar 20, 2024
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Binary file modified book/_build/.doctrees/environment.pickle
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2 changes: 1 addition & 1 deletion book/_build/html/_sources/sampling.md
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Expand Up @@ -188,7 +188,7 @@ Thus, the SE for the percentage of members with an Apple Watch based on the samp

**Adjustment 2**. The SE formulas we first learned assume draws are made *with replacement*. Simple random samples are done without replacement. While we found SE to be about 4.9%, we should note that if a sample of 100 members were done without replacement, we'd have sampled the entire population and there would be no variability in the sample percentage. We'd always find 40% of members have an Apple Watch. This reveals that sampling without replacement actually has a lower associated standard error. The is corrected by a correction factor:

$$\text{SE drawing without replacement = correction factor \times SE drawing with replacement}.$$
$$\text{SE drawing without replacement = correction factor} \times \text{SE drawing with replacement}.$$

And the correction factor is

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2 changes: 1 addition & 1 deletion book/_build/html/sampling.html
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Expand Up @@ -631,7 +631,7 @@ <h4>Finding the right SE<a class="headerlink" href="#finding-the-right-se" title
<p>Thus, the SE for the percentage of members with an Apple Watch based on the sample of 100 members, drawn with replacement is about <span class="math notranslate nohighlight">\(\frac{4.9}{100}\times 100\%\)</span>, or 4.9%.</p>
<p><strong>Adjustment 2</strong>. The SE formulas we first learned assume draws are made <em>with replacement</em>. Simple random samples are done without replacement. While we found SE to be about 4.9%, we should note that if a sample of 100 members were done without replacement, we’d have sampled the entire population and there would be no variability in the sample percentage. We’d always find 40% of members have an Apple Watch. This reveals that sampling without replacement actually has a lower associated standard error. The is corrected by a correction factor:</p>
<div class="math notranslate nohighlight">
\[\text{SE drawing without replacement = correction factor \times SE drawing with replacement}.\]</div>
\[\text{SE drawing without replacement = correction factor} \times \text{SE drawing with replacement}.\]</div>
<p>And the correction factor is</p>
<div class="math notranslate nohighlight">
\[\text{correction factor} = \sqrt{\frac{\text{Population Size - Sample Size}} {\text{Population Size} -1}}.\]</div>
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2 changes: 1 addition & 1 deletion book/sampling.md
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Expand Up @@ -188,7 +188,7 @@ Thus, the SE for the percentage of members with an Apple Watch based on the samp

**Adjustment 2**. The SE formulas we first learned assume draws are made *with replacement*. Simple random samples are done without replacement. While we found SE to be about 4.9%, we should note that if a sample of 100 members were done without replacement, we'd have sampled the entire population and there would be no variability in the sample percentage. We'd always find 40% of members have an Apple Watch. This reveals that sampling without replacement actually has a lower associated standard error. The is corrected by a correction factor:

$$\text{SE drawing without replacement = correction factor \times SE drawing with replacement}.$$
$$\text{SE drawing without replacement = correction factor} \times \text{SE drawing with replacement}.$$

And the correction factor is

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