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 = 23, SSAB = 173. 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 = _________.

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 =__________.

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 =_____________.

Answer 1

Source	SS	df	MS	F	p vlaue
factor A	28	3	9.33	3.86	0.022
factor B	23	2	11.50	4.76	0.018
interaction	173	6	28.83	11.93	0.000
error	58	24	2.42
total	282	35

value of test statistic for factor A =3.86

p value =0.022

because the p value <0.05 , factor A is significant

value of test statistic for factor B =4.76

p value =0.018

because the p value <0.05 , factor B is significant

value of test statistic for interaction =11.93

p value =0.000

because the p value <0.05 , interaction is significant