Statistics

  Let XI, , X.„ be a random sample taken from a Norma/(ps. a2) distribu-tion with some known a. The testing is done between Ho : p = po and HI : p = pi where pi > po. The rejection region of the test is defined as (X > k) for sonic constant k. Suppose that the significance level a is specified. Prove that the power of this test can be written as power = 1 — 4F (4r-`(1 a) aR/Ti Po) where $ denotes the cdf of the standard normal distribution.