The Greek Council is comparing the mean GPAs of four sororities on campus. The G
ID: 3396624 • Letter: T
Question
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
Explanation / Answer
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 39Related Questions
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