Z-Test Calculator
Perform a one-sample or two-sample z-test when the population standard deviation is known. Enter your sample statistics, choose your tail type, and get the z-statistic and p-value instantly.
A z-test is a hypothesis test that uses the standard normal distribution. It is appropriate when the population standard deviation is known and the sample size is large enough (typically n > 30).
One-Sample Z-Test: z = (x̄ - μ₀) / (σ / √n)
Tests whether a sample mean differs significantly from a hypothesized population mean.
Two-Sample Z-Test: z = (x̄₁ - x̄₂) / √(σ₁²/n₁ + σ₂²/n₂)
Tests whether two population means are different.
Choosing a Tail Type
- Two-tailed: Tests if the means are different in either direction (H₁: μ ≠ μ₀)
- Left-tailed: Tests if the mean is less than the hypothesized value (H₁: μ < μ₀)
- Right-tailed: Tests if the mean is greater than the hypothesized value (H₁: μ > μ₀)
When to Use a Z-Test vs. T-Test: Use a z-test when you know the population standard deviation. Use a t-test when you only have the sample standard deviation (which is almost always the case in practice).