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Two groups of children were shown a commercial. One group (the video only group) was shown only the video portion of the commercial, and the second group (the AN group) was shown the ad with both audio and video.
Following the viewing, the children were asked to recall 10 specific items from the ad. A researcher used a small sample t-test to test the null hypothesis Ho: (u1 - u2) = 0, where u1, denotes the mean number of ads recalled by children in the video-only group and u2 denotes the mean for the A/V group. He failed to reject Ho and concluded that there is no difference between the means. Summary statistics for the study are reproduced in the accompanying table. The validity of the inference derived from the test is based on the assumption of equal variances (sigma1^2 = sigma2^2). Complete parts a through e below.
a. Set up the null and alternative hypotheses for testing this assumption.
b. Compute the test statistic.
c. Find the rejection region for the test using alpha = 0.05.
d. Make the appropriate conclusion in the words of the problem.