Solution (source code)

= Solution

The first likelihood-ratio test compares
$$
H_0:\beta_{\rm pollution}=\beta_{\rm risk2}=0
$$
with 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 with
$$
H_0:\beta_{\rm pollution:risk}=0
$$
against a model with a pollution-by-risk interaction. Its $\chi^2_1$ likelihood-ratio p-value is $0.871$, so there is no evidence for an interaction.