Question

The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST = 269, SSA = 26, SSB = 21, SSAB = 171. Set up the ANOVA table. (Round your values for mean squares and F to two decimal places, and your p-values to three decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Factor A
Factor B
Interaction
Error
Total

Test for any significant main effects and any interaction effect. Use α = 0.05.

Find the value of the test statistic for factor A. (Round your answer to two decimal places.)

Find the p-value for factor A. (Round your answer to three decimal places.)

p-value =

State your conclusion about factor A.

Because the p-value > α = 0.05, factor A is not significant.Because the p-value > α = 0.05, factor A is significant.    Because the p-value ≤ α = 0.05, factor A is significant.Because the p-value ≤ α = 0.05, factor A is not significant.

Find the value of the test statistic for factor B. (Round your answer to two decimal places.)

Find the p-value for factor B. (Round your answer to three decimal places.)

p-value =

State your conclusion about factor B.

Because the p-value ≤ α = 0.05, factor B is significant.Because the p-value ≤ α = 0.05, factor B is not significant.    Because the p-value > α = 0.05, factor B is not significant.Because the p-value > α = 0.05, factor B is significant.

Find the value of the test statistic for the interaction between factors A and B. (Round your answer to two decimal places.)

Find the p-value for the interaction between factors A and B. (Round your answer to three decimal places.)

p-value =

State your conclusion about the interaction between factors A and B.

Because the p-value ≤ α = 0.05, the interaction between factors A and B is not significant.Because the p-value > α = 0.05, the interaction between factors A and B is significant.    Because the p-value ≤ α = 0.05, the interaction between factors A and B is significant.Because the p-value > α = 0.05, the interaction between factors A and B is not significant.

Answer 1

Source	SS	df	MS	F	p vlaue
factor A	26	3	8.67	4.08	0.018
factor B	21	2	10.50	4.94	0.016
interaction	171	6	28.50	13.41	0.000
error	51	24	2.13
total	269	35

value of test statistic for factor A =4.08

p value =0.018

because the p value <0.05 , factor A is significant

value of test statistic for factor B =4.94

p value =0.016

because the p value <0.05 , factor B is significant

value of test statistic for interaction =13.41

p value =0.00

because the p value <0.05 , interaction is significant