I In the following study, two new diets (Diet A and Diet B) designed to reduce the Blood Cholesterol level in patients presently suffering from a high Cholesterol level were being assessed. Also included in the experiment was a Standard diet. The researcher also considered Sex (Female, Male) as a factor. The experiment consisted of randomly selecting 5 males suffering from a high Cholesterol level for each of the three diets. Similar samples of females were also selected and assigned to diets. Each patient was required to stay on the diet for a period of one month. At the end of the one month period the, Decrease in Cholesterol level Y, was measured for each subject in the experiment (A negative value for Y indicates and increase in Cholesterol level). The data is tabled below: Female Male Standard -0.40 0.26 3.01 -0.02 -0.70 -6.26 -7.22 -0.63 -2.20 0.02 Diet Diet A 10.18 9.90 16.98 8.55 9.67 11.84 4.61 11.84 11.68 15.21 Diet B 16.40 12.25 12.52 11.72 10.81 5.27 3.50 10.78 10.11 4.70 Let yijk denote the Decrease in Cholestrol level for the kth subject on the jth diet in the ith sex. Where k = 1,2,3,4,5 ; j = 1 (Standard), 2(Diet A), 3(Diet B) and i = 1 (Female), 2(Male). yi... y.j., y... 1. Determine and table the Means y ij., 2. Plot the profiles of the effect of Diet on Decrease in Cholestrol level Y for both females and males. Does it appear that Diet and Sex are interacting factors? 3. Compute Estimates of the main effects of Diet: j = 1 (Standard), 2(Diet A) and 3(Diet B). 4. Compute Estimates of the main effects of Sex: ; i = 1 (Female), 2(Male). ijs 5. Compute Estimates of the interaction effects of Sex and Diet: a; i = 1 (Female), 2(Male) and j = 1 (Standard), 2(Diet A), 3(Diet B).