Question: 15.3. Suppose that X has a Poisson distribution with parameter A. To test Ho: = Ao versus H: A > Ao, the following test is

15.3. Suppose that X has a Poisson distribution with parameter A. To test Ho: = Ao versus H: A > Ao, the following test is proposed. Obtain a sample of size n, compute the sample mean X, and reject Ho whenever > C, where C is a constant to be determined.

(a) Obtain an expression for the OC function of the above test, say L(X). [Hint: Use the reproductive property of the Poisson distribution.]

(b) Graph the OC function. =>

(c) Suppose that we are testing Ho: 0.2 versus H: > 0.2. A sample of size n10 is obtained, and we reject Ho if X> 0.25. What is the significance level of this test?

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