Hypothesis Test for a Mean (z-Test)
Run a full z-test: test statistic, p-value, critical value, decision, and a plain-English conclusion.
Requires σ known (else use the t-test tool). Example: x̄ = 105 vs μ₀ = 100, σ = 15, n = 36, two-tailed, α = 0.05.
① Answer
② Steps
③ Why it works
A hypothesis test asks: if μ really equaled μ₀, how surprising is our x̄? The z-statistic measures the surprise in standard errors. The p-value is the probability of data this extreme under H₀ — small p means H₀ is a bad explanation. We reject H₀ when p < α; otherwise we fail to reject (never “accept” — absence of evidence isn’t evidence of absence).