= 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> is
$$
Y_{it}\overset{\mathrm{ind}}\sim\operatorname{Poisson}(e_{it}e^{\alpha+\beta t}),\qquad\log\mathbb E[Y_{it}]=\log e_{it}+\alpha+\beta t.
$$
The <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 $r=e^\beta$, so
$$
\boxed{\hat r=e^{-0.69901}=0.497077.}
$$
An approximate 95% <Wald confidence interval> transforms the interval for $\beta$:
$$
\boxed{\left[e^{-0.69901-1.96(0.27466)},e^{-0.69901+1.96(0.27466)}\right]=[0.290,0.852].}
$$
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