Draw the “ideal” power curve for the test of Ho'-p < Mo against H\:p > mo-

(That is, consider the best possible situation as far as power is concerned;

for example, what would you like the power to be against any /x > po?)

20.Suppose that X has an exponential distribution with parameter X:

m =

\e Xl 0

if x > 0, elsewhere.

You want to test the hypothesis Hq:\ = 1 against the hypothesis H\:\ = 2, based on a sample of size 1. If

a. = .10, find the region of rejection. What is the probability of making a Type II error? [Hint: Be careful; as the observed value of X gets larger and larger, what is implied about the value of the parameter A?3