An agency offers preparation courses for a graduate school admissions test to students. As part of an experiment to evaluate the merits of the course, 12 students were chosen and divided into 6 pairs...

An agency offers preparation courses for a graduate school admissions test to students. As part of an experiment to evaluate the merits of the course, 12 students were chosen and divided into 6 pairs in such a way that the members of any pair had similar academic records. Before taking the test, one member of each pair was assigned at random to take the preparation course, while the other member did not take a course. The achievement test scores are contained in the Student Pair data file. Assuming

that the differences in scores follow a normal distribution, test, at the 5% level, the null hypothesis that the two population means are equal against the alternative that the true mean is higher for students taking the preparation course.