stats
Z-Test Calculator
One- and two-sample Z-tests — Z-stat, p-value, critical values at α = 0.05/0.01, rejection region curve.
Test Configuration
Test Type
Hypothesis Tail
Sample Data / Summary
Z-test requires known σ. With raw data, σ is estimated from the sample (population formula ÷ n).
Use T-Test when σ is unknown and n is small.
Use T-Test when σ is unknown and n is small.
Results
Z-statistic—
p-value (two-tailed)—
Critical Z α = 0.05—
Critical Z α = 0.01—
Conclusion α = 0.05—
Conclusion α = 0.01—
Z = (x̄ − μ₀) / (σ/√n) · p = 2·(1 − Φ(|Z|))
p-value via Φ(z) = ½·(1 + erf(z/√2))
Abramowitz & Stegun 7.1.26 — max error 1.5 × 10⁻⁷
Abramowitz & Stegun 7.1.26 — max error 1.5 × 10⁻⁷