86. When X1, X2, . . . , Xn are independent Poisson variables, each with parameter l, 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 H0: l  l0, we can replace l by l0 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-daywork 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  .02.