Is it true that the best students sit in the front of a classroom? In a survey done at a university, students reported their grade point averages (GPA) and also answered the question, "Where do you typically sit in a classroom (front, middle, or back)?" A total of 384 students gave valid answers to both questions. The following table summarizes the data obtained in this survey:

Location ni mean GPA, xi

front 88 3.20

middle 218 2.98

back 78 2.92 1

(a) (3 marks) Can the samples be considered random samples? Explain.

(b) (8 marks) Do the survey data provide sufficient evidence that the mean GPA for the populations of students who typically sit in the front, middle, and back of the classroom are not all the same. Conduct a test at significance level = 0.05. (Use F = 6.74, report degrees of freedom, P-value = 0.001).