# solution

Refer to Exercise 9.17. Use a multiple-testing procedure to determine at the Â Â .05 level which of the contrasts is significantly different from zero. Interpret your findings relative to the researchersâ€™ question about finding the most effective weight-loss method.

Exercise 9.17

Refer to Exercise 9.13. Suppose the new weight-loss agents were of the following form:

A1: Drug therapy with exercise and counseling
A2: Drug therapy with exercise but no counseling
A3: Drug therapy with counseling but no exercise
A4: Drug therapy with no exercise and no counseling

Construct contrasts to make comparisons among the agent means that will address the following:

a. Compare the mean for the standard agent to the average of the means for the four new agents.

b. Compare the mean for the agents with counseling to those without counseling. (Ignore the standard.)

c. Compare the mean for the agents with exercise to those without exercise. (Ignore the standard.)

d. Compare the mean for the agents with counseling to the standard.

Exercise 9.13

Researchers conducted an experiment to compare the effectiveness of four new weightreducing agents to that of an existing agent. The researchers randomly divided a random sample of 50 males into five equal groups with preparation A1 assigned to the first group, A2 to the second group, and so on. They then gave a prestudy physical to each person in the experiment and told him how many pounds overweight he was. A comparison of the mean numbers of pounds overweight for the groups showed no significant differences. The researchers then began the study program, and each group took the prescribed preparation for a fixed period of time. The weight losses recorded at the end of the study period are given here:

The standard (existing) agent is labeled agent S, and the four new agents are labeled A1, A2, A3, and A4. Run an analysis of variance to determine whether there are any significant differences among the five weight-reducing agents. Use a Â .05. Do any of the AOV assumptions appear to be violated? What conclusions do you reach concerning the mean weight loss achieved using the five different agents?

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