4. Over the years, the Food and Drug Administration of the United States (FDA) has worked very hard to avoid making type II errors. A type II error occurs when the FDA approves a drug that is not both safe and eective. Despite the agency's efforts, however, bad drugs do on occasion get through to the public. For example, Omniox, an antibiotic, had to be recalled less than six months after its approval due to reports of severe adverse reactions, which included a number of deaths. Similarly, Fenoterol, an inhaled drug intended to relieve asthma attacks, was found to increase the risk of death rather than decrease it. ls there any way for the FDA to completely eliminate the occurrence of type II errors? Explain. 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 is ,u = 219 mg/ 100 ml and the standard deviation is 0' = 43 mg/ 100 ml. Suppose, however, that you do not know the true population mean; instead, you hypothesize that ,u is 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 signicance is appropriate. (a) What is the probability of making a type I error? (b) If a sample of size 29 is selected from the population of men who do not go on to develop coro- nary heart disease, what is the probability of making a type 11 error? Assume the distribution of the serum cholesterol levels is normal. (c) What is the power of the test? (d) How could you increase the power? (e) You wish to test the null hypothesis H0 :p = 244 mg/100 ml against the alternative HA:;1