Confidence Interval for a Proportion

= ± ·

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Example: in a sample of 40 customers, 3 made a complaint. What is the 95% interval for the share of customers who complain? Change the values to work out your own case.

Successes k Sample size n Confidence (%)

Step by step

What each term means

Confidence Interval: The range of plausible values for the proportion in the population. This is the Wald formula, the textbook one; the calculator also shows Wilson's, which behaves better.
Sample Proportion (p̂): The observed share of successes: k divided by n. It is the centre of the Wald interval.
Critical Value (z): It comes from the confidence level: 1.96 for 95%. It says how many standard errors the interval reaches on each side.
Standard Error: How much p̂ varies from sample to sample. With p̂ near 0 or 1 it gets too small, and the Wald interval shrinks just where it should be cautious.