When are independent Poisson variables, each with parameter m, and n is large, the sample mean has approximately a normal distribution with and

. This implies that has approximately a standard normal distribution. For testing , we can replace m by m0 in the equation for Z to obtain a test statistic. This statistic is actually preferred to the large-sample statistic with denominator (when the Xi

’s are Poisson) because it is tailored explicitly to the Poisson assumption. If the number of requests for consulting received by a certain statistician during a 5-day work week has a Poisson distribution and the total number of consulting requests during a 36-week period is 160, does this suggest that the true average number of weekly requests exceeds 4.0? Test using . a 5 .02 S/ 1n H0: m 5 m0 Z 5 X 2 m 2m/n V(X) 5 m/n m 5