Suppose X1,...,Xn are i.i.d. Poisson with unknown mean . The problem is to test = 0

Suppose X1,...,Xn are i.i.d. Poisson with unknown mean θ.

The problem is to test θ = θ0 versus θ>θ0. Consider the test that rejects for large X¯n and the test that rejects for large S2 n = 1 n − 1

n i=1

(Xi − X¯n)

2 .

Compute the Pitman ARE.