Z-Test for a Proportion
Enter the sample proportion p̂, sample size n, hypothesized proportion p₀, significance level α, and the direction of the alternative hypothesis. The calculator computes the standard error √(p₀(1 − p₀)/n), the z statistic, the critical z value and the p-value.
Worked examples
Frequently asked questions
When can I use a z-test for a proportion?
When the sample is large enough that both n·p₀ and n·(1 − p₀) are at least 10, so the sampling distribution of p̂ is approximately normal.
Why is the standard error computed from p₀, not p̂?
Under the null hypothesis the true proportion is p₀, so the SE used for the test statistic uses p₀(1 − p₀). The confidence-interval version of the SE uses p̂(1 − p̂) instead.
Two-tailed vs one-tailed?
Two-tailed rejects on either side; one-tailed only on the specified side. Use a one-tailed test only when there is a substantive reason to care about a specific direction in advance.