Instead of advertising the percentage of customers who improve by at least 10 points, a manager suggests testing whether the mean score improves at all. For each customer they record the difference in score before and after taking the course (After - Before).

a) State the null and alternative hypotheses.

b) The P-value from the test is 0.65. Does this provide any evidence that their course works?

c) From part b, what can you tell, if anything, about the mean difference in the sample scores?