Z-Test for a Single Proportion Calculator
Test a sample proportion against a hypothesized value.
Enter your values
ⓘ Live results
Results
- z-statistic
- 1.6971
- Two-sided p-value
- 0.0897
- Standard error
- 0.03536
- Significant at 0.05?
- No
Quick answer
The z-statistic compares the observed proportion to the hypothesized proportion, scaled by the standard error under the null hypothesis.
z = (p̂-p0)/sqrt(p0(1-p0)/n)
How to use the Z-Test for a Single Proportion Calculator
- 1Enter your observed sample proportion.
- 2Enter the proportion you're testing against (the null hypothesis value).
- 3Enter the sample size — the tool computes the z-statistic and p-value.
Worked example
Using the values the calculator loads with:
Inputs
- Sample proportion0.56
- Hypothesized proportion0.5
- Sample size200
Results
- z-statistic1.6971
- Two-sided p-value0.0897
- Standard error0.03536
- Significant at 0.05?No
Frequently asked questions
When can I use a z-test for proportions?
When np0 and n(1-p0) are both at least 5-10, so the normal approximation holds.
What does a small p-value mean?
Strong evidence that the true proportion differs from the hypothesized value.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.