A dean of a business school claims that the Graduate Management Admission Test (GMAT) scores of applicants to the school’s MBA program have increased during the past 5 years. Five years ago, the mean...

A dean of a business school claims that the Graduate Management Admission Test (GMAT) scores of applicants to the school’s MBA program have increased during the past 5 years. Five years ago, the mean and standard deviation of GMAT scores of MBA applicants were 560 and 50, respectively. Twenty applications for this year’s program were randomly selected and the GMAT scores recorded. If we assume that the distribution of GMAT scores of this year’s applicants is the same as that of 5 years ago, with the possible exception of the mean, can we conclude at the 5% significance level that the dean’s claim is true?