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 = 282, SSA = 28, SSB = 24, SSAB = 176. 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.

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

test statistic =

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 significant.

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

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

Because the p-value > α = 0.05, factor A is significant.

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

test statistic =

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 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.

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

test statistic =

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 significant.

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 not significant.

Because the p-value ≤ α = 0.05, the interaction between factors A and B is significant.

Answer 1

Applying ANOVA:

Source	SS	df	MS	F	p vlaue
factor A	28.00	3	9.33	4.15	0.017
factor B	24.00	2	12.00	5.33	0.012
interaction	176.00	6	29.33	13.04	0.000
error	54.00	24	2.25
total	282.00	35

value of the test statistic for factor A =4.15

p-value =0.017

Because the p-value ≤ α = 0.05, factor A is significant.

value of the test statistic for factor B =5.33

p-value =0.012

Because the p-value ≤ α = 0.05, factor B is significant.

)value of the test statistic for interaction =13.04

p-value = 0.000

Because the p-value < α = 0.05, interaction between factor A and factor B is significant.