Statistics Calculators

One-Sample Z-Test Calculator

Calculate the z-statistic and p-value for a one-sample z-test, comparing a sample mean to a hypothesized population mean with a known population standard deviation.

Z-statistic —

P-value —

P-value (percentage) —

About the One-Sample Z-Test Calculator

The one-sample z-test checks whether a sample mean differs significantly from a hypothesized population mean, when the population standard deviation is known. It's most appropriate for large samples.

Formula: z = (x̄ − μ₀) ÷ (σ ÷ √n)

The resulting z-statistic is converted to a p-value using the standard normal distribution; a small p-value (typically below 0.05) suggests the sample mean is significantly different from the hypothesized value.