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420Exam2Bans - STAT 420 Exam 2(Version B(Answers Fall 2007...

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STAT 420 Fall 2007 Exam 2 ( Version B ) ( Answers ) 1. A two-factor analysis of variance experiment was performed with I = 2, J = 3, and K = 4 ( a 2 × 3 factorial experiment with 4 replicates ) . ANOVA table: Source SS DF MS F Factor A 4 I – 1 = 1 4 2 Factor B 18 J – 1 = 2 9 4.5 Interaction 12 ( I – 1 ) ( J – 1 ) = 2 6 3 Error 36 I J ( K – 1 ) = 18 2 Total 70 I J K – 1 = 23 c) (6) Complete the ANOVA table. d) (6) Conduct the tests of factor interaction and main effects, if appropriate, each at a 5% level of significance. Critical Value Circle one. Interaction F 0.05 ( 2, 18 ) = 3.55 . Significant Not significant Factor A F 0.05 ( 1, 18 ) = 4.41 . Significant Not significant Factor B F 0.05 ( 2, 18 ) = 3.55 . Significant Not significant
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2. The graphs below show the cell means for two-factor replicated experiments. Is there an interaction effect? Factor A main effect? Factor B main effect? a) (2) Interaction Yes No Factor A Yes No Factor B Yes No Lines are NOT parallel ° Interaction A1, A2, A3 – NOT same ° Factor A effect B1, B2, B3 – NOT same ° Factor B effect b) (2) Interaction Yes No Factor A Yes No Factor B Yes No Lines are parallel ° NO Interaction A1, A2, A3 – NOT same ° Factor A effect B1, B2, B3 – same ° NO Factor B effect
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c) (2) Interaction Yes No Factor A Yes No Factor B Yes No Lines are parallel ° NO Interaction A1, A2, A3 – same ° NO Factor A effect B1, B2, B3 – NOT same ° Factor B effect 3.
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