The Greek Council is comparing the mean GPAs of four sororit

The Greek Council is comparing the mean GPAs of four sororities on campus. The GPAs for 10 girls in each sorority are given in the following table. Based on these data, can you conclude that there is a difference between the mean GPAs for these four sororities? Use a 0.05 level of significance.

Sorority GPAs

2.5

3.1

2.7

3.1

3.4

3.4

2.9

3.2

4.0

3.6

2.8

3.1

3.8

3.6

2.8

3.1

2.7

3.7

2.9

2.9

2.8

3.0

3.1

3.1

2.8

4.0

2.9

3.0

3.2

3.9

2.7

3.3

3.1

4.0

2.6

2.7

3.9

3.4

3.3

2.6

Hypotheses:

Test Statistic and value: P-value:

Conclusion

2.5	3.1	2.7	3.1
3.4	3.4	2.9	3.2
4.0	3.6	2.8	3.1
3.8	3.6	2.8	3.1
2.7	3.7	2.9	2.9
2.8	3.0	3.1	3.1
2.8	4.0	2.9	3.0
3.2	3.9	2.7	3.3
3.1	4.0	2.6	2.7
3.9	3.4	3.3	2.6

Solution

Here we want to compare more than 2 population means so one way ANOVA analysis will be used. Hypotheses are:

H0: There is no difference between the mean GPAs for these four sororities.

Ha: There is a difference between the mean GPAs for these four sororities.

Following is the outputof ANOVA analysis generated by excel:

Test statistics:

F=7.4038

P-value of the test is

P-value = 0.00055

Conlusion: Since p-value is less than 0.05 so we reject the null hypothesis. That is on the basis of sample evidence we can conlcude that there is a difference between the mean GPAs for these four sororities.

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Group 1	10	32.2	3.22	0.288444444
Group 2	10	35.7	3.57	0.122333333
Group 3	10	28.7	2.87	0.042333333
Group 4	10	30.1	3.01	0.047666667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	2.78075	3	0.926916667	7.403816286	0.000550228	2.866265557
Within Groups	4.507	36	0.125194444
Total	7.28775	39