The weight-loss business wants to explore whether women and men respond differently to the 3 diets. They collect the data shown below:

a. State the null and alternative hypotheses to be tested to see if there is a difference in the average weight loss for women and men.(If possible, express the hypotheses symbolically).

b. Indicate the p-value for the hypothesis test to test the hypotheses in part a.

c. Using your answer in part b, briefly explain whether or not it can be concluded that there is a difference in the mean weight loss between women and men.

d. State the null and alternative hypotheses to be tested to see if there is an interaction between the diet and sex of the dieters.(If possible, express the hypotheses symbolically).

e. Indicate the p-value for the hypothesis test to test the hypotheses in part d.

f. Based on your answer in part d, indicate what can be determined about the interaction between the diet and the sex of the dieters. Be sure to justify your conclusions based on the hypothesis test.

data : for female:

Diet 1 3.8 6 0.7 2.9 2.8 2 2 8.5 1.9 3.1

Diet 2 -2.1 2 1.7 4.3 7 0.6 2.7 3.6 3 2

Diet 3 7 5.6 3.4 6.8 7.8 5.4 6.8 7.2 7 7.3

for male :

diet 1 -0.6 1.1 4.5 4.1 9 2.4 3.9 3.5 5.1 3.5

diet 2 4.2 2.4 5.8 3.5 5.3 1.7 5.4 6.1 7.9 -1.4

diet 3 2.5 0.9 3.5 0.5 2.8 8.6 4.5 2.8 4.1 5.3