SL 4.11—Hypothesis testing

State $H_0$ and $H_1$, choose significance level $\alpha$, and calculate a test statistic or p-value. Reject $H_0$ when $p\le\alpha$ (or the statistic enters the supplied critical region); otherwise fail to reject $H_0$, always in context.

For a $\chi^2$ independence test, expected frequency is $(\text{row total})(\text{column total})/(\text{grand total})$ and $df=(r-1)(c-1)$. For goodness of fit at SL, $df=n-1$. Expected frequencies exceed 5 in examinations; technology gives $\chi^2$ and the upper-tail p-value.

For the SL t-test, compare two unpaired population means with unknown variance, assume normal underlying variables and equal group variances, and use the pooled two-sample test. Choose one- or two-tailed $H_1$ from the claim, not after viewing the result.

Do not say 'accept $H_0$' or treat significance as practical importance. Poisson-mean tests and Type I/II error calculations belong to AHL 4.18, not this SL Objective.