Show that the test of Problem 7 is uniformly most powerful for testing H0: λ = λ0 versus HA: λ > λ0.
Reference
Let X1, . . . , Xn be a sample from a Poisson distribution. Find the likelihood ratio for testing H0: λ = λ0 versus HA: λ = λ1, where λ1 > λ0. Use the fact that the sum of independent Poisson random variables follows a Poisson distribution to explain how to determine a rejection region for a test at level α.
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