Z-Test Calculator
One-sample z-test from mean, sigma and sample size.
Runs in your browser. Nothing is uploaded — your input is processed on this device and discarded when you close the tab.
Z-Test Calculator
How to use this tool
- Enter the sample mean, the population mean you are testing against, the population standard deviation and the sample size.
- Press Generate. The tool shows the standard error, the z-statistic and the two-tailed p-value.
- Use Load sample for mean 105 against 100 with sigma 15 and n = 36, or Clear to start again.
Worked example
For sample mean 105, population mean 100, sigma 15 and n = 36, the standard error is 15 / sqrt(36) = 2.50, the z-statistic is (105 - 100) / 2.50 = 2.00, and the two-tailed p-value is about 0.0455.
What this tool does not do / Limits
This is a normal-approximation calculation for teaching. It assumes the population standard deviation is known, the sample is random, and either the population is normal or the sample is large enough for the approximation to hold. It is not a substitute for a proper statistical analysis.
Frequently asked questions
When is a z-test the right test?
When the population standard deviation is known and the sample is large or the population is normal. If sigma is estimated from the sample, a t-test is the usual choice instead.
What does the p-value mean here?
Roughly, how surprising the observed mean would be if the null population mean were true. A small p-value means the result is unusual under that assumption — it is not the probability that the null is true.
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