📋 Sampling Distribution of Sample Proportion Calculator
Enter the true population proportion, sample size, and a sample proportion value to find the standard error and the probability of observing that sample proportion or more extreme.
What this calculator does
When you take repeated random samples from a population, the sample proportion (p-hat) varies from sample to sample, forming a sampling distribution. This calculator uses the normal approximation to that sampling distribution to find the probability of observing a given sample proportion or more extreme, based on the true population proportion and sample size.
How the calculation works
The standard error of the sample proportion is SE = sqrt(p(1-p)/n), where p is the population proportion and n is the sample size. The sample proportion value is converted into a z-score using z = (p-hat – p) / SE, and the cumulative standard normal distribution gives the probability either below or above that value, depending on your selection.
The normal approximation works best when both n x p and n x (1-p) are at least 10, which the calculator reports so you can check the approximation is reasonable. This tool is for general statistics education and planning purposes.