1)Body mass index (BMI) 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 BMI is approximately normal with an unknown mean and standard deviation. A sample of 58 men selected from this group has a mean of 25.0 kg/m² and a standard deviation of 2.7 kg/m². At the 5% level of significance, researchers want to test whether the mean baseline BMI for the population of middle-aged men who do develop diabetes is significantly greater than 24.0 kg/m², the mean for the population of men who do not.

a)Explicitly define the population parameter of interest.

b) State the null and alternative hypotheses.

c) State any necessary assumptions.

d) Specify the form of the test statistic and its distribution under the null.

e) State the decision rule and determine the critical region and p-value. (You may want to use R or SAS for calculating critical value and/or p-value.)

f) Construct a 95% confidence interval for the parameter of interest.

g) State your conclusions in the context of the problem.