basic

One-Sample Z-Test Statistic Calculator

z = (x̄ − μ₀) / (σ / √n) — known population SD.

Compute the one-sample z-test statistic for a population mean when σ is known: z = (x̄ − μ₀) / (σ / √n). Compare to ±1.96 for a two-sided 5 % test.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

z = (x̄ − μ₀) / (σ / √n)

In depth

Compute the one-sample z-test statistic for a population mean when σ is known: z = (x̄ − μ₀) / (σ / √n). Compare to ±1.96 for a two-sided 5 % test.