Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 218 / 3 / b / Solution

Overdispersion means that conditional variance exceeds the Poisson mean. Under a correctly specified Poisson model, the Pearson statistic is approximately chi-squared with $149$ residual degrees of freedom. Hereso a one-sided five-percent test rejects. The displayed model-based confidence interval is too narrow. A quasi-Poisson fit can multiply standard errors by $\sqrt{1.3119}$; negative binomial regression or a random-effects count model can model the extra variation directly.