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

Question

Quizplus · Accepted Answer

Since the sample size is less than 30, a t-distribution should be used, and with a significance level of 0.05 and 48 degrees of freedom (n-1 = 49-1), the correct critical value is represented by the t-distribution, not the z-distribution.

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