When X1, X2,..., Xn are independent Poisson variables, each with parameter , and n is large, the

When X1, X2,..., Xn are independent Poisson variables, each with parameter μ, and n is large, the sample mean  has approximately a normal distribution with μ = E() and V() = μ/n. This implies that
Z =  - μ / √μ/n
has approximately a standard normal distribution. For testing H0: μ = μ0, we can replace μ by μ0 in the equation for Z to obtain a test statistic. This statistic is actually preferred to the large-sample statistic with denominator S/√n (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 α = .02.