Body mass index is calculated by dividing a persons 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 developed diabetes mellitus, the distribution of baseline body mass indices is approximately normal with unknown mean ? and standard deviation Ï?. A sample of 58 men selected from this group has mean = 25.0 kg/m2 and standard deviation s = 2.7 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 developed diabetes is equal to 24.0 kg/m2, the mean for the population of 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?