A medical researcher designed an experiment to study the impact of three exercise regimens (30, 60, and 90 minutes per week) on the total blood cholesterol level in active adult males.  The researcher was concerned that the effect of the type of exercise program on cholesterol might also depend on the age of the individual. Nine participants in each of three age groups (A1: 20–29, A2: 30–39, A3: 40–49) were obtained from five fitness centers. The total blood cholesterol level of the participants were measured both prior to the start of the study and after 6 months on the exercise regimens. The reductions in total blood cholesterol level are given in the following table.

a. Identify the design by name.

b. Write a model for this study, identifying all the terms in the model.

c. Do the data support the research hypothesis that the mean reduction in cholesterol increases with an increase in exercise? Use a  .05 in reaching your conclusion.

d. Is your answer in part (c) consistent across all three age groups? Support your answer with a p-value from an appropriate test of hypotheses.

e. Assume that the effectiveness of the three exercise regimens differed for the three age groups. Group the three exercise regimens separately for each age group using an overall Type I error rate of .05.