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 = 274, SSA = 26, SSB = 21, SSAB = 172. 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 Factor A Factor B Interaction Error Total Sum of Squares Degrees of Freedom Mean Square 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 = F State your conclusion about factor A. O Because the p-value ≤ α = 0.05, factor A is significant. O Because the p-value > a = 0.05, factor A is significant. O Because the p-value ≤ a = 0.05, factor A is not significant. O Because the p-value > a = 0.05, factor A is not significant. p-value

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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 = 274, SSA = 26, SSB = 21,
SSAB = 172. 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
Factor A
Factor B
Interaction
Error
Total
Sum
of Squares
Degrees
of Freedom
Mean
Square
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 =
F
State your conclusion about factor A.
O Because the p-value ≤ a = 0.05, factor A is significant.
O Because the p-value > a = 0.05, factor A is significant.
O Because the p-value < a = 0.05, factor A is not significant.
O Because the p-value > a = 0.05, factor A is not significant.
p-value
Transcribed Image Text: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 = 274, SSA = 26, SSB = 21, SSAB = 172. 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 Factor A Factor B Interaction Error Total Sum of Squares Degrees of Freedom Mean Square 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 = F State your conclusion about factor A. O Because the p-value ≤ a = 0.05, factor A is significant. O Because the p-value > a = 0.05, factor A is significant. O Because the p-value < a = 0.05, factor A is not significant. O Because the p-value > a = 0.05, factor A is not significant. 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 =
State your conclusion about factor B.
O Because the p-value ≤ a = 0.05, factor B is not significant.
Because the p-value ≤ a = 0.05, factor B is significant.
Because the p-value > a = 0.05, factor B is significant.
Because the p-value > a = 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 ≤ a = 0.05, the interaction between factors A and B is not significant.
Because the p-value > a = 0.05, the interaction between factors A and B is significant.
Because the p-value ≤ a = 0.05, the interaction between factors A and B is significant.
Because the p-value > a = 0.05, the interaction between factors A and B is not significant.
Transcribed Image Text: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. O Because the p-value ≤ a = 0.05, factor B is not significant. Because the p-value ≤ a = 0.05, factor B is significant. Because the p-value > a = 0.05, factor B is significant. Because the p-value > a = 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 ≤ a = 0.05, the interaction between factors A and B is not significant. Because the p-value > a = 0.05, the interaction between factors A and B is significant. Because the p-value ≤ a = 0.05, the interaction between factors A and B is significant. Because the p-value > a = 0.05, the interaction between factors A and B is not significant.
Expert Solution
Step 1

Given that, The calculations for a factorial experiment involving four levels (p = 4) of factor A, three levels (q = 3) of factor B, and three replications ( m = 3) resulted in the following data: SST = 274, SSA = 26, SSB = 21, SSAB = 172.

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