High school juniors planning to attend college were randomly assigned to view one of four videos that emphasized social life, athletics, scholarship, or artistic/cultural opportunities at a particular college. After viewing the videos, the participants took a test of their desire to attend this college, with the following results. Using the .05 significance level, did the type of activity emphasized in the video affect the participants' desire to attend the college?
Social Life Athletics Scholarship Art/Cultural
66 74 87 72
75 73 78 81
69 79 75 70
78 70 76 69
a. Use the five steps of hypothesis testing.
b. Sketch the distributions involved.
c. Figure the effect size of this study and indicate whether it is nearer to small, medium, or large.
d. Conduct a planned contrast for the Social Life versus Scholarship films (using the .05 level).
e. Conduct Scheffé's test for the groups in (d) and indicate the F cutoff, the F you would use for the comparison, and the hypothesis-testing decision (reject or do not reject).
f. Explain the logic of what you did to a person who is familiar with the t test for independent means, but who knows nothing about the analysis of variance. (Be sure your explanation includes the logic of comparing within-groups to between-groups population variance estimates, the logic of how each of these is figured, the F distribution, and the F table.)
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