Z Test Calculator
Run a one-sample z test when the population standard deviation is known, with p-value, decision, effect direction and student-friendly interpretation.
Formula / method
z = (x̄ − μ₀)/(σ/√n).
Use when σ is known and the sampling assumptions are appropriate.
How to use
Use data from the same population, sample or study definition and keep paired observations aligned.
Understanding a Z test
Use a one-sample Z test when you are testing a population mean against a hypothesized value and the population standard deviation is known (or the model assumptions otherwise justify the Z procedure). The test statistic measures how many standard errors the observed sample mean is from the null value.
How to read the p-value
Compare the p-value with your preselected significance level α. A p-value at or below α is evidence against the null hypothesis under the model assumptions. It is not the probability that the null hypothesis is true.
Before using the result
Check independence, sampling/design assumptions and whether a one-sided alternative was chosen before seeing the data.
What this calculator answers
The Z Test Calculator uses the requested values to calculate the requested result. The core method is z = (x̄ − μ₀)/(σ/√n).. This makes the assumptions visible so you can check whether the inputs match your situation.
How to get a useful result
Use data from the same population, sample or study definition and keep paired observations aligned.
How to interpret it
Statistical output describes the entered sample/model. It does not by itself prove causation, practical significance or that model assumptions are satisfied.
Before relying on the number
Recheck unusual inputs, confirm units and compare the result with any official quote, statement, specification or rule that applies to the real decision. Small changes in rates, time periods or measurements can materially change some results.