Let X1,..., Xm be a random sample from a Poisson distribution with parameter µ1, and let Y1,..., Yn be a random sample from another Poisson distribution with parameter µ2. We wish to test H0: µ1 - µ2 = 0 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 V() = µ/n 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.):

Frequency 0 Region 1 28 40 28 17 8 2 1 1 m=125 Region 2 14 25 30 18 49 21 n-140 8 1