A random sample of nine students was selected to test for the effectiveness of a special course designed to improve memory. The following table gives the scores in a memory test given to these students before and after this course.

a. Construct a 95% confidence interval for the mean d of the population paired differences, where a paired difference is defined as the difference between the memory test scores of a student before and after attending this course.
b. Test at a 1% significance level whether this course makes any statistically significant improvement in the memory of all students.
Assume that the population of paired differences has a normal distribution.

Before 43 57 48 65 81 49 38 69 58 After 49 56 77 89 57 36 64 69