Sample Size for Desired Margin of Error¶
Overview¶
We determine the minimum sample size needed to achieve a desired margin of error.
For a Mean¶
\[
n = \left(\frac{z_{\alpha/2} \cdot \sigma}{E}\right)^2
\]
where \(E\) is the desired margin of error.
For a Proportion¶
\[
n = \left(\frac{z_{\alpha/2}}{E}\right)^2 \hat{p}(1-\hat{p})
\]
Using \(\hat{p} = 0.5\) gives the most conservative (largest) sample size.