Question

12. ANALYSIS OF VARIANCE

The average of grade point averages (GPAs) of college courses in a specific major is a measure of difficulty of the major. An educator wishes to conduct a study to find out whether the difficulty levels of different majors are the same. For such a study, a random sample of major grade point averages (GPA) of 8 graduating seniors at a large university is selected for each of the four majors mathematics, English, Education, and Biology Test, at the 5% level of significance, whether the data contain sufficient evidence to conclude that there are differences among the average major GPAs of these four majors.
MAJORS

Mathematics	English	Education	Biology
2.5	3.6	4.0	2.7
3.1	3.1	3.5	3.5
2.9	3.1	2.8	2.6
2.5	3.7	2.3	3.1
2.5	3.0	3.4	2.9
3.2	2.6	3.5	2.3
2.5	3.2	3.7	2.5
3.1	3.3	3.7	3.2

Answer 1

Solution:

ANOVA table Using Excel:

Here p-value<alpha(0.02<0.05),

here reject Null hypothesis.

conclude that there are not differences among the average major GPAs of these four majors.