Researchers conducted an experiment to compare the effectiveness of four new weight- ­reducing 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 = .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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A 124 10.7 11.9 11.0 124 .3 13.0 12.5 13.1 A2 9.1 15 .7 132 10.7 10.6 11.3 111.7 9.9 11.3 10,5 11.2 A 127 132 118 12.2 113.7118 12.2 11.7 8.7 9.3 82 83 9.0 94 92 12.2 85 9.9 8.5 11.6 102 10.9 0 9.6