Refer to the American Heart Association Conference (Nov. 2005) study to gauge whether animal-assisted therapy can improve the physiological responses of heart failure patients, presented in Exercise. Recall that 76 heart patients were randomly assigned to one of three groups. Each patient in group T was visited by a human volunteer accompanied by a trained dog, each patient in group V was visited by a volunteer only, and the patients in group C were not visited at all. The anxiety level of each patient was measured (in points) both before and after the visits. The accompanying table gives summary statistics for the drop in anxiety level for patients in the three groups. The mean drops in anxiety levels of the three groups of patients were compared with the use of an analysis of variance. Although the ANOVA table was not provided in the article, sufficient information is given to reconstruct it.

a. Compute SST for the ANOVA, using the formula (on p. 484)

Where x̄ is the overall mean drop in anxiety level of all 76 subjects.
b. Recall that SSE for the ANOVA can be written as

Where s12, s22, and s32 are the sample variances associated with the three treatments. Compute SSE for the ANOVA.
c. Use the results from parts a and b to construct the ANOVA table.
d. Is there sufficient evidence (at α = .01) of differences among the mean drops in anxiety levels by the patients in the three groups?
e. Comment on the validity of the ANOVA assumptions. How might this affect the results of the study?

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Sample Mean Std. Size Drop Dev. Group T: VolunteerTrained Dog 26 05 7.6 3.9 7.5 Group V: Volunteer only Group C: Control group (no visit) 25 14 25 SSE = (n1-1)y? + (n2-1)s: + (n3-1)s