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Z-test

The z-test compares means using the standard normal distribution, and is used when the population standard deviation (σ) is known — usually from previous research. This calculator runs two variants: one-sample (compare a sample mean to a known value, μ0) and two-sample (compare the means of two independent groups). If σ is unknown, use the t-test instead.

How to use the z-test calculator

  1. Choose the test with the buttons at the top.
  2. Enter the known population SD (σ) — for the two-sample test, one for each group.
  3. Enter the data — raw values in the grid (one or two columns depending on the test) or summarized statistics (x̄, n).
  4. Choose the tails and the significance level, and for the one-sample z-test, the expected mean (μ0).
  5. Open More options to set the expected difference, rounding, outliers and effect size.
  6. Press Calculate.

Assumptions

  • Normal distribution (or a large sample, based on the central limit theorem).
  • The population standard deviation (σ) is known.
  • Independent observations; for the two-sample test, independent groups.

Example: a farmer calculated last year the average weight of the apples in his orchard, μ0 = 17 kg, based on the entire population, and knows the standard deviation from previous research. This year he checked a small sample with an average of x̄ = 18 kg. Has the average weight changed this year?