Question: When testing H0 : = 0 versus HA : 6= 0 at = 0.05 with n = 100, suppose that , the probability of a

When testing H0 : = 0 versus HA : 6= 0 at = 0.05 with n = 100, suppose that , the probability of a type II error, is equal to 0.04 when = 2. Which of the following statements are true?

I) < 0.04 when = 1

II) < 0.04 if the sample size was only 50

III) < 0.04 if had been half as large

IV) The power of the test at = 2 is 0.96

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