Z-Test Calculator
Tests a sample mean against a fixed value when the standard deviation is known in advance.
p-value
—
Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
z statistic —
Standard error —
Reading this —
The formula
z = (x̄ − μ₀) ÷ (σ ÷ √n)
A known σ is rare outside standardised tests and some process control.
What to watch out for
For large samples, z and t give nearly the same answer. The p-value calculator explains how to read the result.
Frequently Asked Questions
What is a worked example?
A sample mean of 105 from 50 values, against 100 with a standard deviation of 15, gives z = 2.357 and a two-sided p of 0.018422.
What about percentages?
Use the proportion z-test, which is built for those.