Assume Y1 Y2 Yn is a random sample of size n from a Poisson

Assume Y1, Y2, …, Yn is a random sample of size n from a Poisson() distribution. Using each of the methods below, develop a test of H0 : = 0 vs. H1 : 0 using = 0.05. (a) Wald test (b) Likelihood ratio test (c) Score test (d) Exact test (Hint: The sum of n independent Poisson random variables each with mean has a Poisson distribution with mean n. For this exact test, just describe in words what you would do.)

Solution