The standard ±1.645 SD approach to binomial distribution confidence intervals breaks down with small samples or extreme proportions. The Wilson score interval, proposed in 1927, handles both cases gracefully. This post walks through a practical call center QA example with formulas and a ready-made calculator.

A radio host saw 4 listener texts for and 4 against, and called the audience evenly split. The math says otherwise: on a sample of 8, the true share is anywhere from 21% to 79%. Here’s how to compute that – and why you’d need 271 texts.

A contractor claims every fifth call has a bad connection. How many good calls in a row do you need to disprove him? This post uses a binomial hypothesis test to calculate the exact sample size for 99% confidence — with the Google Sheets formula included.