Question

Using the data below, answer the question: Is there a significant difference in the GPAs of students who graduate in three years vs four years vs five or more years? Use the five steps for hypothesis testing to make your decision. Remember the "Sesame Street" song!

Years to Graduate	N	Mean	Standard deviation
3	8	3.66	0.28
4	26	2.81	0.59
5 or more	8	2.66	0.42

Source	Sum of Squares	df	Mean Squares
Between Groups	5.24	2	2.617
Within Groups	10.52	39	0.28

Answer 1

Hypothesis:

Ho: There is not significant difference in the GPAs of students who graduate in three years vs four years vs five or more years

Ha: There is a significant difference in the GPAs of students who graduate in three years vs four years vs five or more years

Level of significance () = 0.05

ANOVA TABLE:

Test statistic = F = Mean square Between group / Mean square Within group = 2.617 / 0.28 = 9.346

Critical value:

Ftabulate = F,(t-1,n-t) = F0.05,(2,39) = 3.238                             ..............Using F table

Conclusion:

Test statistic > Critical value, i.e. 9.346 > 3.238, That is Reject Ho at 5% level of significance.

Therefore, There is a significant difference in the GPAs of students who graduate in three years vs four years vs five or more years