Testing math skills: In order to test the effectiveness of a program to improve mathematical skills, a simple random sample of 45 fifth graders was chosen to participate in the program. The students were given an exam at the beginning of the program and again at the end. The sample mean increase in the exam score was 12.2 points, with a sample standard deviation of 4.7 points.

a. Construct a 99% confidence interval for the mean increase in score.

b. The developers of the program claim that the program will produce a mean increase of more than 15 points. Does the confidence interval contradict this claim? Explain.