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 this is approximately normal with unknown mean µ and standard deviation ? . a sample of 58 min selected from this group has mean body mass index is calculated by dividing a person =25.0 kg/m2 and standard deviation s=2.7 kg/m2.

(a) construct a 95% confidence interval for the population mean µ.

(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 24.0 kg/m2, the mean for the population of men who do not. what is the p-value of the test?

(c) what do you conclude?

(d) based on the 95% confidence interval, would you have expected to reject or not to reject the null hypothesis? why?