The director of admissions of a distinguished MBA program is interested in studying the proportion of entering students in similar graduate business programs who have achieved a composite score on the Graduate Management Admissions Test (GMAT) in excess of 630. Specifically, the admissions director believes that the proportion of students entering top-rated graduate programs with such composite GMAT scores is higher in 2016 than it was in 2012.

To test this hypothesis, he has collected random samples of MBA candidates entering his program in the fall of 2016 and in the fall of 2012. He believes that these GMAT scores are indicative of the scores earned by their peers in his program and in competitors' programs. The GMAT scores for the random students entering in each year are provided on the left.

Question

10-07-2024
Mathematics

High School

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The director of admissions of a distinguished MBA program is interested in studying the proportion of entering students in similar graduate business programs who have achieved a composite score on the Graduate Management Admissions Test (GMAT) in excess of 630. Specifically, the admissions director believes that the proportion of students entering top-rated graduate programs with such composite GMAT scores is higher in 2016 than it was in 2012.

To test this hypothesis, he has collected random samples of MBA candidates entering his program in the fall of 2016 and in the fall of 2012. He believes that these GMAT scores are indicative of the scores earned by their peers in his program and in competitors' programs. The GMAT scores for the random students entering in each year are provided on the left.

Answer :

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TerryMartha TerryMartha · Answer 1 · 2024-09-18T04:56:08-04:00

The director is comparing the proportion of high-scoring students in 2016 and 2012 to determine if there is a significant difference.

To perform the hypothesis test, the director collected random samples of MBA candidates entering the program in both years.

The proportions of students with GMAT scores above 630 are calculated for each year. Statistical techniques, such as a test of proportions (e.g., z-test or chi-square test), can be employed to compare the proportions and assess if the difference is statistically significant.

By analyzing the test statistic and comparing it to the appropriate critical value or p-value, the director can make a conclusion about whether the proportion of high-scoring students differs significantly between 2016 and 2012.

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