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 |
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.
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