The following contingency table shows the distribution of grades earned by students taking a midterm exam in an MBA class, categorized by the number of hours the students spent studying for the exam:

Grade Time Spent Studying A B C Less than 3 hours 4 18 8 3–5 hours 15 14 6 More than 5 hours 18 12 5

a. Using a = 0.05, perform a chi-square test to determine if a student’s grade on the exam and the hours spent studying for it are independent of one another.

b. What conclusions can be made based on these results?

c. Verify your results using PHStat.

AppendixLO1