# Managers of a firm are trying

Managers of a firm are trying to determine which of threeprograms is the best. They believe that the effectiveness of theprograms may be influenced by sex and interaction. A factorialexperiment was performed and you are given the following ANOVAtable: Source of Variation Sum of Squares df Mean Square F FactorA: Programs 31 3 * * Factor B: Sex 11 1 * * Interaction 1.5 3 * *Error 4.5 4 * Total 48 11 What advice would you give managers aboutthe influence of sex and interaction? Use a .05 level ofsignificance.

Complete ANOVA table is given below

 Source of Variation Source of Variation df Mean Square F P.Value Factor A: Programs 31 3 10.33 9.14159292 0.0291 Factor B: Sex 11 1 11 9.734513274 0.0355 Interaction 1.5 3 0.5 0.442477876 0.7355 Error 4.5 4 1.13 Total 48 11

where  Mean Square = (Sourceof Variation / df)

FA= (Mean Square Factor A: Programs / MeanSquare Error)

F B= (Mean Square Factor B: Sex/ Mean SquareError)

FAB= (Mean Square Interaction/ Mean SquareError)

P.Values are calculated from F-Table for particularvalue for degrees of freedoms.

Calculated p.value for Factor B: Sex = 0.0355 which isless then 0.05 imply that Factor B: Sex have significant effect onthe effectiveness of the programs while as p.value for interaction= 0.7355  which is much greater then 0.05 imply thatinteraction have not significant effect on the effectiveness of theprograms.

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