Free · Probability and statistical models

Proportion Margin of Error with Population Correction

Estimate a normal-approximation margin for a sampled proportion.

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With 50 successes in 100 observations and the retained 95% critical value 1.96, the uncorrected margin is 9.8 percentage points.

MOE = z √(p(1−p)/n); finite correction = √((N−n)/(N−1))

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Independent random sampling and an adequate number of successes and failures are assumed.
Critical values in the selector are rounded. A normal interval is unreliable for small samples and proportions near zero or one.
The population correction assumes sampling without replacement from a finite population. Sample size cannot exceed population size.
The retained input domain excludes proportions exactly zero or one and zero successes. Population and sample values must be positive.

Independent random sampling and an adequate number of successes and failures are assumed.

Require whole positive sampling counts; retain the captured strict interior proportion domain.