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p-Value Calculator (One-Proportion z-Test)

Test whether a sample proportion differs from a baseline — z statistic, one/two-sided p-value, and a plain-language decision.

Also available in 한국어

Calculator inputs
The amounts you entered are included in the link. Anyone with the link sees the same result.
p-value
0.10960
Test statistic z
1.6000
Decision at 5% level
Fail to reject

How it was calculated

  1. 01Test statistic z

    z = (p̂ − p0) / √(p0(1−p0)/n) = (0.58 − 0.5) / 0.050000

    Basis: One-proportion z-test (large-sample normal approximation)

    1.6
  2. 02p-value = 0.10960 (10.9599%)

    2 × (1 − Φ(|z|)) = 2 × (1 − Φ(1.6000))

    Basis: Standard normal CDF Φ — alternative hypothesis Two-sided: p ≠ p0

    10.96%
  3. 03Significance decision (α = 5%)

    p ≥ 0.05 → fail to reject the null — the observed difference is within chance

    Basis: Significance level α = 0.05 (0.01/0.10 depending on the study)

  4. 04Interpretation caveat

    The p-value is not 'the probability the null is true' but 'the probability of a result at least this extreme under the null'. Large samples make trivial differences significant — check effect size too

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