In a study of students at Lewis & Clark Community College, a professor compared the chosen seat location of students in mathematics courses to their overall grade point average (GPA). He randomly selected 10 students from each of three seat locations: (1) front, (2) middle, and (3) back. The GPAs follow:

(a) Explain why this data may be analyzed using a one-way ANOVA.
(b) Test the null hypothesis that the mean score for each location is the same at the a = 0.05 level of significance.
(c) If the null hypothesis is rejected in part (a), use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05.
(d) Draw boxplots of the three treatment levels to support the analytic results obtained in parts (b) and (c).

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Front Middle Back 2.598 2.690 3.080 3.523 2.937 2.879 3.332 3.091 2.926 3.885 2.655 3.221 3.559 2.526 2.646 3.062 2.859 2.583 3.894 2.639 2.653 2.966 3.634 3.090 3.575 3.564 3.060 4.000 2.115 2.463