<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. Here
$$
X^2=149(1.3119)\simeq195.5,\qquad
\frac{X^2-149}{\sqrt{2(149)}}\simeq2.69>1.645,
$$
so 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.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-218/3/b/solution