Question

Complete the analysis of variance table for the following data. Treat it as a two       way Block Design.  (Use α = 0.05). In each cell there are 2 observations, except for         the last cell, which has only one observation. DATA             Source A Means I II III Source B Level 1 20    18 12    14 9    11 14 Source B Level 2 12    10 10      8 8 9.6 Means 15 11 9.33 Grand Mean = 12 ANOVA TABLE Sources D.F. S.S. M.S. F Source A Source B Error TOTAL State the Alternate Hypothesis  Ha  for both sources of variability. Source A   Ha:                                             Source B    Ha: How many degrees of freedom for A? …….        What is the Critical Point for A?............   How many degrees of freedom for B? …….        What is the Critical Point for B?............ Do you reject Ho for Source A?  ……..                  Do you reject Ho for Source B?  …….. So, is Source A statistically significant? …………..      And Source B? ………………..

Answer 1

We used technology to perform ANOVA for given data and the obtained ANOVA table is given below:

ANOVA table
	D.F.	S.S.	M.S.	F
Source A	2	61.33	30.67	8.26
Source B	1	66.67	66.67	17.95
Error	7	26	3.71
Total	10	154

Answer(a):

Source A: we have to test

H0: there is no difference in means of three levels of Factor A (i.e. µI=µII=µIII)

Ha: there is significant difference in means of at least one level of Factor A (i.e. at least one µA is different)

Source B: we have to test

H0: there is no difference in means of two levels of Factor B (i.e. µ1=µ2)

Ha: there is significant difference in means of at least one level of Factor B (i.e. at least one µB is different)

Answer(b):

Degrees of freedom for A = nA – 1 = 3 -1 = 2        

The Critical Point for A = F(0.95,2,7) = 4.74

Answer(c):

Degrees of freedom for B = nB – 1 = 2 - 1 = 1       

The Critical Point for B = F(0.95,1,7) = 5.59

Answer(d):

For Source A, we have Fcalculated = 8.256, which is greater than Fcritical = 4.74 at α=0.05 and it suggests that we have strong evidence against H0 to reject it, so we reject H0 for Source A.

The answer is YES

For Source B, we have Fcalculated = 17.95, which is greater than Fcritical = 5.59 at α=0.05 and it suggests that we have strong evidence against H0 to reject it, so we reject H0 for Source B.

The answer is YES

Answer(e):

For Source A, since we have rejected the H0 we can conclude that the source B is statistically significant at α=0.05.

The Answer is YES

For Source B, since we have rejected the H0 we can conclude that the source A is statistically significant at α=0.05

The Answer is YES