Sample Size to Estimate Proportion Formula

Given below sample size formula to estimate a proportion with specified precision. The desired precision of the estimate will be half the width of the desired confidence interval (i.e) for an example if you give the desired precision of 5%, you would get the confidence interval width to be about 0.1 (10%.). Refer the below sample size to estimate proportion formula with the desired precision and confidence, for both an infinite population and for a population of the specified size.


Population Sample Size (n) = (Z2 x P(1 - P)) / e2


Z = Z Score of Confidence Level
P = Expected Proportion
e = Desired Precision
N = Population Size
For small populations n can be adjusted so that n(adj) = (Nxn)/(N+n)

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Sample size to estimate proportion formula is defined as (Z2 x P(1 - P)) / e2. Population sample size is based on the true portion, confidence level, desired precision and population size.

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