A Tutor Promises to Improve GMAT Scores of Students by More

Multiple Choice

A tutor promises to improve GMAT scores of students by more than 50 points after three lessons. To see if this is true, the tutor takes a sample of 49 students' test scores after and before they received tutoring. The mean difference was 53 points better after tutoring, with a standard deviation of the difference equal to 12 points. Let µ_D denote the mean of the difference: score after tutoring minus score before tutoring. Which of the following is the appropriate conclusion at the 5% significance level?

A) Reject H₀; we can conclude that the mean difference in test scores after and before tutoring is greater than 50 points.
B) Reject H₀; we cannot conclude that the mean difference in test scores after and before tutoring is greater than 50 points.
C) Fail to reject H₀, we can conclude that the mean difference in test scores after and before tutoring is greater than 50 points.
D) Fail to reject H₀; we cannot conclude that the mean difference in test scores after and before tutoring is greater than 50 points.