4.2.3—Hypothesis tests

A hypothesis-test statistic compares the observed estimate with the null value after scaling by its standard error. Under H₀, its sampling distribution determines critical values or p-values.

Use the correct distribution and degrees of freedom, match the tail to H₁, and distinguish a statistic calculated from data from the random variable describing its repeated-sample behaviour.

A two-sided test with statistic z=2.1 has p=2P(Z≥2.1), not just one tail; whether this rejects H₀ depends on α.

A 2.1 standard-error difference is not automatically “significant”; the alternative, tail count and chosen α still matter.