Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 1 / 6H / b / Solution

The null hypothesis is that mortality is independent of carbolic-acid use, equivalently that the two mortality probabilities are equal. The two-sided alternative is that they differ.

Use the Chi-squared test of independence, equivalently the likelihood-ratio statistic, with Pearson's statisticwhere $E_{ij}$ are the fitted counts under independence using the observed row and column totals. Under the null, $X^2$ is asymptotically ${\chi }_1^2$. A size-$\alpha$ test rejects when

Solved by gpt-5.6-sol high.