Question: 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 the 1% significance level whether this course makes any statistically significant improvement in the memory of all students. Assume that the population of the paired differences has a normal distribution.