6.5.4—Hypothesis tests

For testing μ=μ₀ with known σ, use Z=(X̄−μ₀)/(σ/√n). If σ is estimated and the syllabus model requires it, use the corresponding t statistic.

State H₀, calculate the standard error, choose the tail and compare with the correct critical value. The observed mean is evidence, not the null value itself.

With x̄=52, μ₀=50, σ=10, n=100, z=2; the decision depends on α and whether the test is one- or two-sided.

Using σ instead of σ/√n understates the evidence by ignoring the sample size.