Let X1, , Xn be i i d with the Poisson distribution having mean Let Y a Suppose that we wish to test the hypotheses H0 1 versus H1 1 Show that the test reject H0 if Y 0 is uniformly most powerful level 0 for some number 0 Also find 0 b Find the power function of the test from part (a)

Question: Let X1, . . . , Xn be i.i.d. with the Poisson distribution having mean . Let Y = a. Suppose that we wish to

Let X1, . . . , Xn be i.i.d. with the Poisson distribution having mean θ. Let Y =
a. Suppose that we wish to test the hypotheses H0 : θ ≥ 1 versus H1 :θ < 1. Show that the test “reject H0 if Y = 0” is uniformly most powerful level α0 for some number α0. Also find α0.
b. Find the power function of the test from part (a).

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