Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 13L / e / Solution

The first likelihood-ratio test compareswith the alternative that at least one is nonzero. The deviance drop $73.5-55.3=18.2$ is compared with ${\chi }_2^2$, giving $p=0.000114$; there is strong evidence that the covariates improve the model.

The second test compares the additive model withagainst a model with a pollution-by-risk interaction. Its ${\chi }_1^2$ likelihood-ratio p-value is $0.871$, so there is no evidence for an interaction.