Suppose $X_1, X_2, \ldots, X_n$ is an iid random sample from an Poisson distribution with mean $\lambda$. Let $\lambda_0 < \lambda_1$. Show that the test with significance level $\alpha$ for testing $H_0 : \lambda = \lambda_0$ versus $H_a : \lambda = \lambda_1$ specified by the Neyman-Pearson Lemma is equivalent to rejecting $H_0$ when $\bar{X} \ge k$, where $k$ is chosen so that $P(\bar{X} \ge k \ | \ H_0) = \alpha$.