Question

Complete the following table and test whether there is a difference among the group means at a 0.025 level of significance.

Source	df	SS	MS	F
Among Groups		787.5		3.5
Within Groups	16	1200
Total

Answer 1

Solution:

MS(within) = 1200/16 = 75

Now , F = MS(among)/MS(within)

So , MS(among) = F * MS(within) = 3.5 * 75 = 262.5

Now ,

MS(among) = SS(among)/df(within)

So , df(among) = 787.5/262.5 = 3

df(Total) = 3 + 16 = 19

	df	SS	MS	F
Among Groups	3	787.5	262.5	3.5
Within Groups	16	1200	75
Total	19

= 0.025

Critical value = F_{0.025 , 3 , 16} = 4.08

F= 3.5 < Critical value = 4.08

Fail to reject the null hypothesis.

There is no significant difference among the group means