Question: (Requires short answer to each parts of the question, including the results of the statistical test as well as your interpretation for parts (a) and (b).

Last fall, a sample of n = 25 freshmen was selected to participate in a new 4-hour training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshmen class. All freshmen must take the same English Language Skills course, and the mean score on the final exam for the entire program had a mean score was µ = 74. The students in the new program had a mean score of M = 78 with SS = 2400.

(a) On the basis of these data, can the college conclude that the students in the new program performed significantly better than the rest of the freshmen class? Use a one-tailed test \(\alpha \) = .05

(b) Can the college conclude that the students in the new program are significantly different from the rest of the freshman class? Use a two-tailed test with \(\alpha \) = .05.