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HW Solutions Stat 88

HW Solutions Stat 88 - Chapter 25 RANDOM AND MIXED EFFECTS...

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Chapter 25 RANDOM AND MIXED EFFECTS MODELS 25.5. b. H 0 : σ 2 µ = 0, H a : σ 2 µ > 0. F = . 45787 /. 03097 = 14 . 78 , F ( . 95; 5 , 114) = 2 . 29. If F 2 . 29 conclude H 0 , otherwise H a . Conclude H a . P -value = 0+ c. ¯ Y .. = . 22767, n T = 120, s { ¯ Y .. } = . 06177, t ( . 975; 5) = 2 . 571, . 22767 ± 2 . 571( . 06177), . 0689 µ . . 3865 25.6. a. F ( . 025; 5 , 114) = . 1646, F ( . 975; 5 , 114) = 2 . 680, L = . 22583 , U = 4 . 44098 . 1842 σ 2 µ σ 2 µ + σ 2 . 8162 b. χ 2 ( . 025; 114) = 90 . 351, χ 2 ( . 975; 114) = 145 . 441, . 02427 σ 2 . 03908 c. s 2 µ = . 02135 d. Satterthwaite: df = ( ns 2 µ ) 2 ÷ [( MSTR ) 2 / ( r 1) + ( MSE ) 2 /r ( n 1)] = [20( . 02135)] 2 ÷ [( . 45787) 2 / 5 + ( . 03907) 2 / 6(19)] = 4 . 35 , χ 2 ( . 025; 4) = . 484, χ 2 ( . 975; 4) = 11 . 143 . 0083 = 4 . 35( . 02135) 11 . 143 σ 2 µ 4 . 35( . 02135) . 484 = . 192 MLS : c 1 = . 05, c 2 = . 05, MS 1 = . 45787, MS 2 = . 03907 , df 1 = 5, df 2 = 114, F 1 = F ( . 975; 5 , ) = 2 . 57 , F 2 = F ( . 975; 114 , ) = 1 . 28, F 3 = F ( . 975; , 5) = 6 . 02 , F 4 = F ( . 975; , 114) = 1 . 32, F 5 = F ( . 975; 5 , 114) = 2 . 68 , F 6 = F ( . 975; 114 , 5) = 6 . 07, G 1 = . 6109,
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