Last fall, a sample of n = 30 freshman 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 freshman class. All freshman must take the same English Language Skills course, and the mean population score on the final exam for the entire freshman class was µ = 74 (assume ? is unknown). The sample of students (n = 30) in the new program had a mean score of M = 84 with a standard deviation of s = 18. Using a one-sample t-test, evaluate the hypothesis that the new training program had an influence on performance in the English Language Skills course.
a. Using symbols, state the hypotheses (H0 and H1) for a two-tailed test.
b. Find the critical value/region for an ? = .01 for a two-tailed test.
c. Calculate the test statistic (t-statistic) for the sample.
d. Make a decision and write a conclusion statement for your result.