Question

Given the following analysis of variance​ table, compute mean squares for between groups and within groups. Compute the F ratio and test the hypothesis that the group means are equal.

Source of Variation	Sum of Squares	Degrees of Freedom
Between groups	903	3
Within groups	559	13
Total	1,462	16

State the null and alternative hypotheses. Choose the correct answer below.

H0:?

H1:?

Compute mean squares for between groups and within groups and compute the F ratio.

Source of Variation	Sum of Squares	Degrees of Freedom		Mean Squares		F Ratio
Between groups
Within groups	903		3
Total	559		13
	1,462		16

Determine the critical​ value,

Upper F Subscript Upper K minus 1 comma n minus Upper K comma alpha(FK−1,n−K,α)​,

at the 0.01 level of significance.

Upper F Subscript Upper K minus 1 comma n minus Upper K comma alpha(FK−1,n−K,α)equals=5.?

Test the hypothesis that the group means are equal at the

0.010.01

level of significance.

Since the F ratio is (greater/less)=?  than

Upper F Subscript Upper K minus 1 comma n minus Upper K comma alpha(FK−1,n−K,α​), (reject/do not reject)=?  the null hypothesis. There is (sufficient/unsufficient)=? evidence to conclude that there is a difference in the group means.

Answer 1

Ho : There is no significant difference in the group means i.e. (since k = 4 )

Ha : There is significant difference in the group means i.e. atleast two group means are significantly different from each other.

Level of significance (l.o.s.) : = 0.01

Decision criteria : Reject Ho at 5% l.o.s. if Fcal > Fcrit , where Fcrit = FK-1, N-k ,   = F3 , 13 , 0.01 = 5.739 ( from the F table of 1% points )

Calculations : We know that,

Mean sum of squares = Sum of squares / degrees of freedom

and Fcal = Mean sum of squares for between groups / Mean sum of squares for Within group

Source of variation	Sum of squares	degrees of freedom	Mean sum of squares	Fcal	Fcrit
Between groups	903	K-1 = 3	301	7	5.739
Within group	559	N-K = 13	43
Total	1462	N-1 = 16

Conclusion : Since Fcal > Fcrit, we reject Ho at 5% l.o.s. and thus, conclude that there is significant difference in the group means i.e. atleast two group means are significantly different from each other.