Question 4 X is normally distributed with unknown mean, u and known standard deviation (=10). A sample of n = 25 is selected. A hypothesis test is performed at α = 0.05 to test: Ho=78 versus H: <78. a) Find the power of the test if the true population mean is 75. (CO2-3 MARKS) b) Now the test is performed at a = 0.01, find the power of the test. (CO2-3 MARKS) c) Sketch the power function when α = 0.05 versus 0.01. (CO2-2 MARKS) d) Draw the normal distribution plots to show the critical region and power of test for part (a) and (b). Compare and comment on the power of the test for both cases. (CO2-5 MARKS)