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When testing H0 : µ = 0 versus HA : µ 6= 0 at α = 0.05 with n = 100, suppose that β, the probability of a type II error, is equal to 0.04 when µ = 2. Which of the following statements are true?
I) β < 0.04 when µ = 1
II) β < 0.04 if the sample size was only 50
III) β < 0.04 if σ had been half as large
IV) The power of the test at µ = 2 is 0.96
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