In order to determine whether or not a driver's education course improves the scores on a driving exam, a sample of 6 students were given the exam before and after taking the course. The results are shown below.
Student Score before the course Score after the course
1 83 87
2 89 88
3 93 91
4 77 77
5 86 93
6 79 83
a. What is the average improvement on the scores after taking the course?
b. At 90% confidence using the critical value approach, test to see if taking the course actually increased scores on the driving exam.