# 420Pr1ans - 1 a y= 7 62 5 54.8 6 53 = 57 18 SSB = 7 62 57 2...

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1. a) y = 18 53 6 8 . 54 5 62 7 + + = 57 . SSB = 7 ( 62 – 57 ) 2 + 5 ( 54.8 – 57 ) 2 + 6 ( 53 – 57 ) 2 = 295.2 . SSW = 6 31 + 4 34.7 + 5 28 = 464.8 . ANOVA table: Source SS DF MS F Between 295.2 2 147.6 4.7633 Within 464.8 15 30.98667 Total 760.0 17 H 0 : μ 1 = μ 2 = μ 3 vs. H 1 : at least two of μ i are different. F 0.05 ( 2, 15 ) = 3.68. Reject H 0 at α = 0.05 . F 0.01 ( 2, 15 ) = 6.36. Accept H 0 at α = 0.01 . b) ( 29 ( 29 = = - - - ± I i i i pooled I i i i n c s c I I N I F 1 2 1 1 , 1 Y γ , where pooled s = MSW . c 1 = 1, c 2 = 2 1 - , c 3 = 2 1 - . n i 7 5 6 i y 62 54.8 53 = = ± 3 1 2 3 1 2 98667 . 30 68 . 3 i i i i i i n c y c 8.1 ± 7.3 ( 0.8 , 15.4 )

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2. a) H 0 : μ 1 = μ 2 = μ 3 H a : at least two of μ i are different J = 3. N = n 1 + n 2 + … + n J = 5 + 5 + 5 = 15. 15 3 . 2 5 3 . 3 5 5 . 2 5 ... 2 2 1 1 + + = + + + = N n n n J J y y y y = 2.7. SSB = ( 29 ( 29 ( 29 2 2 2 2 2 1 1 ... y y y y y y J J n n n - + + - + - = 5 ( 2.5 – 2.7 ) 2 + 5 ( 3.3 – 2.7 ) 2 + 5 ( 2.3 – 2.7 ) 2 = 2.8. MSB = 2 8 . 2 1 SSB = - J = 1.4. SSW = ( 29 ( 29 ( 29 2 2 2 2 2 1 1 1 ... 1 1 J J s n s n s n - + + - + - = 4 0.220 + 4 0.235 + 4 0.145 = 2.4. MSW = 12 4 . 2 SSW = - J N = 0.2. SSTot = SSB + SSW = 2.8 + 2.4 = 5.2. F = 2 . 0 4 . 1 MSW MSB = = 7 . ANOVA table: Source SS DF MS F Between 2.8 2 1.4 7 Within 2.4 12 0.2 Total 5.2 14 Critical Value(s): F 0.05 ( 2, 12 ) = 3.89 . Decision: Reject H 0 at α = 0.05 .
( 29 ( 29 H B 2 H B 1 1 MSW d.f. α t n n y y J N + - ± - t 0.025 ( 12 ) = 2.179. ( 29 3 . 2 3 . 3 - ± 5 1 5 1 2 . 0 179 . 2 + 1.0 ± 0.6163 c) ( 29 ( 29 = = - - - ± J j j j J j j j n c y c J J N J F 1 2 1 1 MSW , 1 α c F = 0, c B = 1, c H = – 1. F 0.05 ( 2, 12 ) = 3.89. ( 29 3 . 2 3 . 3 - ± + 5 1 5 1 2 2 . 0 89 . 3 1.0 ± 0.7889 d) c F = – ½ , c B = 1, c H = – ½ . + - 2 3 . 2 5 . 2 3 . 3 ± + + 20 1 5 1 20 1 2 2 . 0 89 . 3 0.9 ± 0.6832 e) ( 29 j i pooled J N J j i n n s q 1 1 2 Y Y , , + ± - - γ 12 , 3 , 05 . 0 q = 3.77. ( 3.3 – 2.3 ) ± 5 1 5 1 2 . 0 2

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420Pr1ans - 1 a y= 7 62 5 54.8 6 53 = 57 18 SSB = 7 62 57 2...

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