Suppose, to be specific, that in Problem 12, 00= 1, n = 10, and that a = .05. In order to use the test, we must find the appropriate value of c.

a Show that the rejection region is of the form {  x0}  {  x1}, where x0 and x1are determined by c.

b Explain why c should be chosen so that P (exp(—)  c) = .05 when 0 = 1.

c Explain why Xi and hence  follow gamma distributions when 0= 1. How could this knowledge be used to choose c?

d Suppose that you hadn't thought of the preceding fact. Explain how you could determine a good approximation to c by generating random numbers on a computer (simulation).

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