Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 37 / 4 / b / Solution

Let $Y_{it}$ be the accident count at location $i$ in period $t\in \{0,1\}$, and $e_{it}$ its exposure in years, where $t=1$ denotes after installation. The Poisson exposure model isThe offset $\log e_{it}$ has its coefficient fixed at one. The model assumes constant rates within each period, a common before rate across locations, a common treatment rate ratio, independent counts, and Poisson variance equal to the mean. The incidence rate ratio is $r=e^{\beta }$, soAn approximate 95% Wald confidence interval transforms the interval for $\beta$: