Chief executive officers of hospitals are adopting unconventional therapeutic methods to shorten the length of stay of patients. At an American Heart Association Conference (Nov. 2005), a study to gauge whether animal-assisted therapy can improve the physiological responses of heart failure patients was presented. In the study, 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 table below 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 using an analysis of variance. Although the ANOVA table was not provided in the article, sufficient information is provided to reconstruct it.

a. Compute SST for the ANOVA, using the formula

where is the overall mean drop in anxiety level of all 76 subjects. [Hint: = (ˆ‘3i=1 ni,(i,)/76.]
b. Recall that SSE for the ANOVA can be written as SSE = (n1 - 1]s21 + (n2 - 1)s22 + (n3 - 1)s23
where s21, s22, and s23 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 Size Mean Drop Std. Dev Group T: Volunteer + Group V: Volunteer Group C: Control Trained Dog only group(no visit) 26 25 25 105 3.9 1.4 76 7.5 7.5