The two-sample z-test in Section 5-2 can be viewed as a large sample test for the difference in means.

Suppose that we need to compare the means of two independent Poisson distributions. Let be a random sample from a Poisson distribution with mean 1 and let be a random sample from a Poisson distribution with mean 2. In applying the z-test we could take advantage of the fact that in the Poisson distribution both the mean and variance of the distribution are equal to .

Develop a variant of the z-test appropriate for this situation.

Develop a large-sample CI for the difference in Poisson means.