Body mass index is calculated by dividing a person's weight by the square of his or her height; it is a

measure of the extent to which the individual is overweight. For the population of middle-aged men who

later develop diabetes mellitus, the distribution of baseline body mass indices is approximately normal

with an unknown mean and standard deviation . A sample of 45 men selected from this group has

mean = 27.0 kg/m2 and standard deviation s = 3.3 kg/m2.

a. Construct a 95% confidence interval for the population mean .

b. At the 0.05 level of significance, test whether the mean baseline body mass index for the

population of middle-aged men who do develop diabetes is equal to 25.0 kg/m2, the mean for the

population of men who do not. What is the p-value of the test?