Question 11.80

highschoolgpa

5. Grades and the SAT. In its “Profile of College-Bound Seniors,” the College Board provided the following data on high school grade point average and gender for the students taking the SAT exam. We are interested in testing whether the proportion of females is the same across the six grade categories.

High school grade point average
Gender A+ A A− B C D–F
Female 60 62 59 53 43 43
Male 40 38 41 47 57 57
  1. Before you perform any calculations, what result might we expect? Examine the table carefully to see whether you can identify any differences in the proportions of females.
  2. Test whether the proportion of females is the same across the six grade categories, using level of significance .

11.99.5

(a) A higher proportion of the females with high GPAs take the SAT exam than the proportion of the females with lower GPAs. (b) . : Not all the proportions in are equal. Reject if -value . Since none of the expected frequencies is less than 1 and none of the expected frequencies is less than 5, the conditions for performing the test for homogeneity of proportions are met. . -value . Since the -value , we reject . There is evidence that the proportion of females is not all the same across the six grade categories.