diff --git a/book/_build/.doctrees/environment.pickle b/book/_build/.doctrees/environment.pickle index 55abbd9..c48b259 100644 Binary files a/book/_build/.doctrees/environment.pickle and b/book/_build/.doctrees/environment.pickle differ diff --git a/book/_build/.doctrees/sampling.doctree b/book/_build/.doctrees/sampling.doctree index c41e062..4b77fe0 100644 Binary files a/book/_build/.doctrees/sampling.doctree and b/book/_build/.doctrees/sampling.doctree differ diff --git a/book/_build/html/_sources/sampling.md b/book/_build/html/_sources/sampling.md index 2a939e6..cecb0bf 100644 --- a/book/_build/html/_sources/sampling.md +++ b/book/_build/html/_sources/sampling.md @@ -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 diff --git a/book/_build/html/sampling.html b/book/_build/html/sampling.html index fe5080d..a112038 100644 --- a/book/_build/html/sampling.html +++ b/book/_build/html/sampling.html @@ -631,7 +631,7 @@

Finding the right SEThus, the SE for the percentage of members with an Apple Watch based on the sample of 100 members, drawn with replacement is about \(\frac{4.9}{100}\times 100\%\), or 4.9%.

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

\[\text{correction factor} = \sqrt{\frac{\text{Population Size - Sample Size}} {\text{Population Size} -1}}.\]
diff --git a/book/images/.DS_Store b/book/images/.DS_Store index 2a19201..37f0057 100644 Binary files a/book/images/.DS_Store and b/book/images/.DS_Store differ diff --git a/book/sampling.md b/book/sampling.md index 2a939e6..cecb0bf 100644 --- a/book/sampling.md +++ b/book/sampling.md @@ -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