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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.