stats

One-Sample Proportion Test

Z-test for a proportion against a known value — p-value, Wilson CI, reliability check, rejection-region curve.

Inputs

Successes x

Sample size n

Hypothesized proportion p₀

Hypothesis tail

Confidence level

Results

Sample proportion p̂—

Std error SE—

Z-statistic—

p-value (two-tailed)—

95% CI lower (Wilson)—

95% CI upper (Wilson)—

Conclusion α = 0.05—

Conclusion α = 0.01—

Z = (p̂ − p₀) / √(p₀(1−p₀)/n)
Wilson CI: (p̂ + z²/2n ± z√(p̂(1−p̂)/n + z²/4n²)) / (1 + z²/n)

SE uses H₀ proportion p₀ for the test; Wilson CI uses p̂.
Reliability check: n·p₀ ≥ 5 and n·(1−p₀) ≥ 5.