5. Data from the Framingham Study allow us to compare the distributions of initial serum cholesterol levels for two populations of males: those who go on to develop coronary heart disease and those who do not. The mean serum cholesterol level of the population of men who do not develop heart disease isu = 219 mg/100 ml and the standard deviation is o = 41 mg/100 ml. Suppose, however, that you do not know the true population mean; instead, you hypothesize that equal to 244 mg/100 ml. This is the mean initial serum cholesterol level of men who eventually develop the disease. Since it is believed that the mean serum cholesterol level for the men who do not develop heart disease cannot be higher than the mean level for men who do, a one-sided test conducted at the a = 0.05 level of significance is appropriate. is (a) What is the probability of making a type I error? (b) If a sample of size 25 is selected from the population of men who do not go on to develop coronary heart disease, what is the probability of making a type II error? (c) What is the power of the test? (d) How could you increase the power? (e) You wish to test the null hypothesis Ho : µ > 244 mg/100 ml against the alternative HA : µ < 244 mg/100 ml at the a = 0.05 level of significance. If the true population mean is as low as 219 mg/100 ml, you want to risk only a 5% chance of failing to reject Ho. How large a sample would be required? (f) How would the sample size change if you were willing to risk a l0% chance of failing to reject a false null hypothesis?