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

= 205mg/10ml and the standard deviation is = 36mg/100ml. Suppose, however, that you do not know

the true population mean; instead, you hypothesize that is equal to 228mg/100ml. 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 = 0.05 level of significance is

appropriate.

a. What is the probability of making a type I error?

b. If a sample of size 30 is selected from the population of men who do not go on to develop

coronary heart disease, what is the power of the test?

c. What is the probability of making a type II error?