Question: Assume that X1, . . . , X9 are i.i.d. having the Bernoulli distribution with parameter p. Suppose that we wish to test the hypotheses

Assume that X1, . . . , X9 are i.i.d. having the Bernoulli with parameter p. Suppose that we wish to test the hypotheses
H0: p = 0.4,
H1: p = 0.4.
Let Y =
a. Find c1 and c2 such that
Pr(Y ≤ c1|p = 0.4) + Pr(Y ≥ c2|p = 0.4)
is as close as possible to 0.1 without being larger than 0.1.
b. Let δ be the test that rejects H0 if either Y ≤ c1 or Y ≥ c2.What is the size of the test δc?
c. Draw a graph of the power function of δc.

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