The 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 has an unknown mean and a standard
deviation . A sample of 58 men selected from this group has mean 25.0 kg/m2 and
a standard deviation 2.7 kg/m2.
(a) Construct a 95% confidence interval for the population mean .
(b) At the 0.05 significance level, test whether the mean baseline body mass index
for the population of middle-aged men who do develop diabetes is greater than
24.0 kg/m2, which is the mean for the population of men who do not develop
diabetes.