= Solution
Under the two-rate alternative, maximize the <piecewise-exponential survival model> likelihood separately to obtain the estimates in part (i). Under $H_0:\theta_1=\theta_2=\theta$, there are 15 deaths and 2200 days of exposure, so $\widehat\theta=15/2200$. Twice the maximized log-likelihood difference is
$$
2\left[
7\log\frac7{400}+8\log\frac8{1800}
-15\log\frac{15}{2200}
\right].
$$
Under the null this <likelihood-ratio test> statistic is asymptotically $\chi_1^2$.
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