A Recent College Graduate Is in the Process of Deciding

Essay

A recent college graduate is in the process of deciding which one of three US graduate schools he should apply to. He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT) scores of those who are accepted into the school. A random sample of six students in each school produced the following GMAT scores. $$\begin{array} { | c | c | c | } \hline &{ \text { GMAT Scores } } \\\hline \text { School 1 } & \text { School } 2 & \text { School } 3 \\\hline 650 & 510 & 590 \\\hline 620 & 550 & 510 \\\hline 630 & 700 & 520 \\\hline 580 & 630 & 500 \\\hline 710 & 600 & 490 \\\hline 690 & 650 & 530 \\\hline\end{array}$$ Assuming that the data are normally distributed, can he infer at the 10% significance level that the GMAT scores differ among the three schools?