Problem 5 [34 points]: Suppose we are interested in the factors affecting the honour classification of students from a university. 600 alumni, who were graduated from 3 different colleges over the past summer, were sampled from the university. The number of students by College, Gender and Honour Classification are displayed in the table below: Honour Classifications of Student's Degree 1st Class 2nd Class Honour 2nd Class Honour 3rd Class College Gender Honour (Upper Divison) (Lower Divison) Honour Total A Male 10 28 45 7 90 Female 13 29 58 10 110 B Male 6 18 58 18 100 Female 5 22 56 17 100 C Male 10 15 40 15 80 Female 15 25 60 20 120 Total 59 137 317 87 600 (a) [16 points] Test the hypothesis on whether the Honour Classification is different across gender at a = 0.05. (b) [18 points] Test the hypothesis on whether the Honour Classification is different across the 3 colleges at a = 0.05