Question: Let {X1, X2, . . . , X25} be a random sample of size n = 25 from N(, 2 ), where 2 = 3.24

Let {X1, X2, . . . , X25} be a random sample of size n = 25 from N(, 2 ), where 2 = 3.24 is known. A researcher decides to test: H0 : = 15 vs. H1 : < 15 using a 1% significance level. i. Calculate the power of the test when = 14.7. (6 marks) ii. Briefly explain in two different ways how you could increase the power of this test.

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