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Question 1 Suppose X ∼ N(µ, 100). To test H0 : µ = 83.4 against Ha...

Question 1 Suppose X ∼ N(µ, 100). To test H0 : µ = 83.4 against Ha : µ > 83.4, let the critical region be defined by R = {x : x > 86.6}, where x is the sample mean of size n = 25 from this distribution. (a) What would be the decision if P25 i=1 Xi = 2050? [3 Marks] (b) What is the level of significance for this test? [3 Marks] (c) Define the power function for this test. Evaluate it at the points 83, 84, 85, 86, 87, 88, 89, 90, 91 and hence produce a graph of the power function. [5 Marks]

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