Question 5

A college professor wishes to find out whether the difficulty levels of different majors are the same. A random sample of major grade point averages (GPA) of 11 students at his university is selected for four majors: business, sociology, computer science, and arts. The data are given in the table below. At the 5% level of significance, test whether the data contain sufficient evidence to conclude that there are differences among the average major GPAs of these four majors.

Business Sociology Computer science Arts 3.13 4.00 3.59 3.57 2.50 3.30 2.39 3.22 3.29 2.61 3.74 2.32 3.17 3.78 3.77 3.21 3.88 3.19 4.00 3.23 2.59 3.64 2.80 3.51 2.97 3.03 3.47 3.16 2.64 3.15 3.59 2.78 2.70 3.20 3.47 2.65 2.53 3.54 3.13 2.94 2.53 3.25 3.00 2.58