A study was designed to evaluate the effectiveness of new treatments to reduce the systolic blood pressure of patients determined to have high blood pressure. Three drugs were selected for evaluation (D1, D2, and D3). There are numerous nondrug treatments for reducing blood pressure, including various combinations of a controlled diet, exercise programs, biofeedback, and so on. The researchers randomly selected three nondrug treatments (ND1, ND2, and ND3) for examination in the study. The age of the patient often may hinder the effectiveness of any treatment. Thus, patients with high blood pressure were divided into two age groups (A1 and A2). A group of 54 patients was divided into the two age groups and then randomly assigned to a combination of one of the three drugs and one of the three nondrug treatments. After patients had participated in the program for 2 months, the reductions in their systolic blood pressure readings from their blood pressure readings at the beginning of the program were recorded. These values are given in the following table.

a. Write a model for this study. Identify all the terms in your model, and state all the necessary conditions placed on the terms in the model.

b. Construct the AOV table for the study, including the expected mean squares.

c. Test the significance of all relevant sources of variation. Use a  .05.

d. What conclusions do you draw about the differences in the effectiveness of the combinations of nondrug and drug treatments for high blood pressure?

e. Would it be appropriate to recommend a treatment based on these data? Justify your answer.