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education/statistics/Sampling.md
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@ -38,6 +38,8 @@ An ideal sample will represent the whole population.
## Percentages
(Ch 20, stat 1040)
Throughout this chapter, percentages are often represented by referencing a box model of 1s and 0s, where 1s are datapoints that *are* counted, and 0s are datapoints that are not counted.
The expected value for a sample percentage equals the population percentage. The standard error for that percentage = `(SE_sum/sample_size) * 100%`.
To determine by how much the standard error is affected, if $n$ is the proportion that the population changed by, the standard error will change by $\frac{1}{\sqrt{n}}$.
@ -46,4 +48,9 @@ Accuracy in statistics refers to how small the standard error is. A smaller stan
You can use the below equation to find the percentage standard error of a box model that has ones and zeros. the % of ones and zeros should be represented as a proportion (EG: `60% = 0.6`).
$$ \sqrt{\frac{(\%\space of\space 1s)(\%\space of\space 0s)}{num_{draws}}} $$
If asked
If asked if an observed % is reasonable, you can calculate the z score, and if the z score is more than 2-3 standard deviations away.
(Ch 23, stat 1040)