Question

A test preparation claims that more than​ 50% of the students who take their test prep course improve their scores by at least 10 points. 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 ​(Afterminus​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?  

Answer 1

We have D= After - Before

Since the hypothesis is to test whether the mean difference is better (it will tell us if scores improve or not)

a) We are testing,

H0: Ud=0 vs H1: Ud>0

b) The p-value of the test is 0.65 is sufficiently large, so we have insufficient evidence to Reject H0. So based on this we do not find any evidence that the course works since we conclude that Ud=0

c) Since we conclude that Ud=0, this tells us that there's no difference in the mean scores of After and Before taking the course.