At Joliet Junior College, the mathematics department decided to offer a redesigned course in Intermediate Algebra, called the Math Redesign Program (MRP). Laura Egner, the coordinator of the program, wanted to determine if the grade distribution in the course differed from that of traditional courses. The following shows the grade distribution of traditional courses based on historical records and the observed grades in three pilot classes in which the MRP program was utilized.

(a) How many students were enrolled in the MRP program for the three pilot courses? Based on this result, determine the expected number of students for each grade assuming there is no difference in the distribution of MRP student grades and traditional grades.
(b) Does the sample evidence suggest that the distribution of grades is different from the traditional classes at the α = 0.01 level of significance?
(c) Explain why it makes sense to use 0.01 as the level of significance.
(d) Suppose the MRP pilot program continues in three more classes with the grades earned for all six pilot courses shown below. Notice that the sample size was simply doubled with the grade distribution remaining unchanged. Does this sample evidence suggest that the distribution of grades is different from the traditional classes at the α = 0.01 level of significance? What does this result suggest about the role of sample size in the ability to reject a statement in the null hypothesis?

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Traditional Distribution Observed Counts in MRP Program A 0.133 7 B 0.191 16 C 0.246 10 D 0.104 13 F W 0.114 0.212 6 12