Question: A sample of N = 36 freshmen was selected to participate in a new 4-hours training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshman class. All freshmen must take the same English language skills course and the mean score of the final exam for the entire freshman class was \(\mu =74\), and the students in the new program had a mean score of \(M=79.4\) with a standard deviation of s = 18.

(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 freshman class? Use a one-tailed test with \(\alpha =0.05\).

(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 \(\alpha =0.05\)