Question: A company sent seven of its employees to attend a course in building self-confidence. These employees were evaluated for their self-confidence before and after attending this course. The following table gives the scores (on a scale of 1 to 15, 1 being the lowest and 15 being the highest score) of these employees before and after they attended the course.
Before 8 5 4 9 6 9 5
After 10 8 5 11 6 7 9
a. Construct a 95% confidence interval for the mean μd of the population paired differences, where a paired difference is equal to the score of an employee before attending the course minus the score of the same employee after attending the course.
b. Test at the 1% significance level whether attending this course increases the mean score of employees. Assume that the population of paired differences has a normal distribution.