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

Answer:

Given ANOVA table is

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

ANOVA table is :

Source	df	SS	MS	F
Among Groups	3	787.5	262.5	3.5
Within Groups	16	1200	75
Total	19	1987.5

Here, H0: there is no difference among the group means.

H1: there is a difference among the group means

Now the critical value is

F(crit) = 4.08 ...( from f distribution table with df n1=3, n2=16 and alpha=0.025)

Also from Excel

=FINV(0.025,3,16) = 4.0768 = 4.08 ( rounded to 2 decimals)

Conclusion:

We know if F> F(crit) then we reject null hypothesis.

As F = 3.5 is less than F(crit) = 4.08, we can not reject the null hypothesis.

Hence we conclude that there is a difference among the group means at a 0.025 level of significance.