How to use it
- Pick the mean or the proportion test.
- Enter the sample result, the value under H₀ and n (and σ for a mean).
- Choose the alternative and α, then read z and p.
How it works
The statistic z measures how many standard errors the sample result is from the null value. The p-value comes from the standard normal distribution: 2 × P(Z > |z|) for two-sided, P(Z > z) for right-sided and P(Z < z) for left-sided.
Worked example
Mean test: x̄ = 105, μ₀ = 100, σ = 15, n = 36. The standard error is 15 / 6 = 2.5, so z = 5 / 2.5 = 2. The two-sided p-value is about 0.0455, which is below 0.05.
Proportion test: 60 successes in 100 trials against p₀ = 0.5 gives a standard error of 0.05 and z = (0.6 − 0.5) / 0.05 = 2, with the same p-value.
Tips
- Decide the alternative before looking at the data; switching to one-sided afterwards halves p unfairly.
- Statistical significance does not mean the difference matters in practice.