One-Sample Mean Z-Test
Test a sample mean when population standard deviation is known.
How the one-sample mean z-test works
A one-sample z-test compares an observed sample mean with a hypothesized population mean when population standard deviation is treated as known. Dividing that deviation by square root n gives the standard error. The signed mean difference divided by standard error is z, and symmetric standard-normal tails beyond its absolute value form the two-tailed p value.
The defaults compare sample mean 105 with hypothesized mean 100, known standard deviation 15, and n equal to 36. Standard error is 15 divided by 6, or 2.5. The verified z statistic is 2, and the standard-normal two-tailed probability is approximately 0.045500264, indicating how unusual that absolute departure is under the null model.
Reading one-sample mean z-test results privately
The population standard deviation must genuinely be known or justified; replacing it with a small-sample estimate calls for a t-test. Observations should be independent, and the sampling distribution of the mean should be approximately normal. A p value is not the probability that the null hypothesis is true and does not communicate practical effect size. This one-sample mean z-test calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
Why is this a z-test instead of a t-test?
The formula treats population standard deviation as known. Estimating spread from a small sample introduces t-distribution uncertainty.
What does a negative z statistic mean?
The sample mean is below the hypothesized mean. A two-tailed test uses the absolute magnitude for its p value.
Is the one-sample mean z-test private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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