🧮 Z-Test Calculator
Run a one-sample z-test to compare your sample mean against a known population mean when the population standard deviation is known.
What the z-test does
The one-sample z-test compares a sample mean to a known or hypothesized population mean when the population standard deviation is known and the sample size is reasonably large. It produces a z-statistic showing how many standard errors apart the two means are.
The formula
z = (x̄ − μ) / (σ / √n), where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. The calculator also estimates a two-tailed p-value using a standard normal approximation.
This calculator is for general educational and planning purposes; for small samples or an unknown population standard deviation, a t-test is usually more appropriate.