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. Assuming α = 0.05, which of the following is the appropriate critical value?

A) z = 1.677
B) z = 2.011
C) t_0.05,48 = 1.677
D) t_0.05,₄₈ = 2.011