What this calculator does
Z-test for a single mean works out tests a sample mean against a hypothesised mean when the population standard deviation is known. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulaz = (x̄ − μ₀) / (σ/√n)
The inputs explained
| Field | What to enter |
|---|---|
| Sample mean | A number. Starts at 104. |
| Hypothesised population mean μ₀ | A number. Starts at 100. |
| Known population standard deviation σ | A number. Starts at 15. |
| Sample size | A number. Starts at 36. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with sample mean
Every other input is held at the calculator’s starting values while sample mean varies. Select any row to load that scenario into the calculator.