Let be a random sample from a Poisson distribution with parameter m1, and let be a random sample from another Poisson distribution with parameter m2. We wish to test against one of the three standard alternatives. When m and n are large, the large-sample z test of Section 9.1 can be used. However, the fact that suggests that a different denominator should be used in standardizing . Develop a large-sample test procedure appropriate to this problem, and then apply it to the following data to test whether the plant densities for a particular species are equal in two different regions (where each observation is the number of plants found in a randomly located square sampling quadrate having area 1 m2

, so for region 1 there were 40 quadrates in which one plant was observed, etc.):