64. Suppose that X, the fraction of a container that is lled, has pdf f (x; u)...

Question:

64. Suppose that X, the fraction of a container that is lled, has pdf f (x; u) uxu1 for 0 x 1 (where u

0), and let X1, . . . , Xn be a random sample from this distribution.

a. Show that the most powerful test for H0: u 1 versus Ha: u 2 rejects the null hypothesis if

b. Is the test described in

(a) UMP for testing H0:

u 1 versus Ha: u 1? Explain your reasoning.

c. If n 50, what is the (approximate) value of c for which the test has signi cance level .05?

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