Question: Suppose X 1 , . . . , X n is a random sample on X which has a N(, 2 0 ) distribution,

Suppose X1, . . . , Xn is a random sample on X which has a N(μ, σ20) distribution, where σ20 is known. Consider the two-sided hypotheses

H0 : μ = 0 versus H1 : μ ≠ 0.

Show that the test based on the critical region C = {|‾X| > √σ20/nzα/2} is an unbiased level α test.

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