In: Statistics and Probability
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 = 275, SSA = 26, SSB = 22, SSAB = 174. 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 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 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 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