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 hypotheses will determine if the students improved their test scores by more than 50 points after being tutored? A) H₀: µ_D ≤ 0, H_A: µ_D 0 B) H₀: µ_D ≥ 0, H_A: µ_D50 D) H₀: µ_D ≥ 50, H_A: µ_D

Question

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 hypotheses will determine if the students improved their test scores by more than 50 points after being tutored? A) H₀: µ_D ≤ 0, H_A: µ_D> 0 B) H₀: µ_D ≥ 0, H_A: µ_D<0 C) H₀: µ_D ≤ 50, H_A: µ_D>50 D) H₀: µ_D ≥ 50, H_A: µ_D<50

Quizplus · Accepted Answer

The correct hypothesis to test if students improved their scores by more than 50 points is to set the null hypothesis (H0) as the mean difference being less than or equal to 50 (indicating no improvement or improvement up to 50 points), and the alternative hypothesis (Ha) as the mean difference being greater than 50 (indicating improvement of more than 50 points).

A Tutor Promises to Improve GMAT Scores of Students by More