One-Sample z-Test
z = (x̄ − μ) / (σ/√n). Compare sample mean to known population.
Result
z-score
2.3570
Two-tail p = 0.018422.
- Sample mean105
- Population μ100
- σ15
- n50
- SE2.1213
- z2.3570
- Two-tail p0.018422
- Sig α=0.05?✓
Step-by-step
- SE = σ / √n = 15 / √50 = 2.1213.
- z = (105 − 100) / 2.1213 = 2.3570.
- p = 2(1 − Φ(|z|)) = 0.0184.
How to use this calculator
- Enter sample mean + population μ + σ + n.
About this calculator
One-sample z-test compares sample mean to a known/hypothesized population mean (with known σ). Used when population SD is known and sample is large (n ≥ 30). Otherwise prefer t-test. Foundational in quality control (process drift detection), educational testing (group vs. norm), epidemiology (incidence comparison). Source: Wolfram MathWorld - Z-Test.
Frequently asked
z: σ known, n large. t: σ estimated from sample. Practically: use t (more conservative, generalizes).
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