What this calculator does
Z-test for a proportion works out tests a sample proportion against a hypothesised population proportion. 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 = (p̂ − p₀) / √(p₀(1−p₀)/n); two-tailed p-value = 2(1 − Φ(|z|))
The inputs explained
| Field | What to enter |
|---|---|
| Sample proportion (p̂) (%) | A number, measured in %. Starts at 58. |
| Hypothesised proportion (p₀) (%) | A number, measured in %. Starts at 50. |
| Sample size | A number. Starts at 150. |
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 proportion (p̂)
Every other input is held at the calculator’s starting values while sample proportion (p̂) varies. Select any row to load that scenario into the calculator.