The two-way table summarizes data from an experiment comparing the effectiveness of three different diets (A, B, and C) on weight loss. Researchers randomly assigned 300 volunteer subjects to the three diets. The response variable was whether each subject lost weight over a 1 year period.

a. Suppose we randomly select one of the subjects from the experiment. Show that the events “Diet B” and “Lost weight” are independent.

b. Copy and complete the table so that there is no association between type of diet and whether a subject lost weight.

c. Copy and complete the table so that there is an association between type of diet and whether a subject lost weight.

Diet Lost A C Total weight? Yes 60 180 No 40 120 Total 90 100 110 300