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 correct value of the test statistic? A) z = 1.7143 B) z = 1.7500 C) t₄₈ = 1.7143 D) t₄₈ = 1.7500

Question

Quizplus · Accepted Answer

The correct test statistic is $t_{48} = 1.7500$. This is because the sample size is relatively small (n=49), and we are dealing with a sample mean difference, making the t-statistic the appropriate choice. The degrees of freedom for the t-test is n-1, which is 48 in this case. The calculation of the exact value of the test statistic isn't provided, but among the options given, the t-statistic with the correct degrees of freedom is the appropriate choice for testing the mean difference in scores.

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