Z-Test Calculator
Calculate a one-sample z statistic and two-tailed p-value.
How the Z-Test Works
The one-sample z test compares a sample mean with a hypothesized population mean when the population standard deviation is known. The statistic is z = (x̄ − μ) / (σ / √n).
When to Use It
Use a z test when observations are independent and the population standard deviation is known, or when a large-sample approximation is appropriate.
FAQ
What does a large absolute z score mean? It indicates the sample mean is far from the hypothesized mean in standard-error units.
How a Z-Test Is Used
A z-test compares an observed mean with a reference value when population variability is known or the sample is large enough for a normal approximation.
Z-Test Example
If a sample mean differs from a claimed population mean, the z statistic expresses that difference in standard-error units.
Interpreting Results
Larger absolute z values generally correspond to smaller p-values. Statistical significance should still be considered together with effect size and study quality.
Frequently Asked Questions
When is a z-test appropriate?
Commonly when population standard deviation is known or large-sample conditions apply.
What does z = 0 mean?
The observed value matches the reference expectation.
Is a z-test the same as a t-test?
No. T-tests account for estimated variability through the t distribution.
Methodology, Assumptions and Interpretation
A z-test standardizes an observed difference by its standard error. It is appropriate when the sampling distribution is adequately normal and the required variance assumptions are met; small samples with unknown variance often call for a t-based method instead.