1 · Observe

Red region: reject H₀. The gold line marks your z-statistic.

2 · Manipulate

3 · Predict

With μ₀ = 100, x̄ = 106, σ = 15, n = 36: before computing, is z closer to 1, 2, or 3? At α = 0.05 two-tailed, would you reject?

4 · See

5 · Explain

The z-statistic measures how many standard errors the sample mean sits from H₀: z = (x̄ − μ₀)/(σ/√n). The p-value is the chance of seeing data this extreme if H₀ were true. If p < α, the data is too surprising under H₀ — reject it. Otherwise we simply fail to reject (we never “accept” H₀).