Question

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A factorial experiment involving two levels of factor A and three levels of factor B resulted in the following data.

		Factor B
		Level 1	Level 2	Level 3
Factor A	Level 1	133	92	75
		163	68	93
	Level 2	127	125	120
		97	103	136

Test for any significant main effects and any interaction. 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 not significant.  

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

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

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

Answer 1

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

2.05

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

p-value = 0.202

State your conclusion about factor A.

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.)

4.06

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

p-value = 0.077

State your conclusion about factor B.

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

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

6.63

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

p-value = 0.030

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.

Source	SS	df	MS	F	p-value
Factor A	588.00	1	588.000	2.05	0.202
Factor B	2,328.00	2	1,164.000	4.06	0.077
Interaction	3,800.00	2	1,900.000	6.63	0.030
Error	1,720.00	6	286.667
Total	8,436.00	11

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