HW Solutions Stat 102

HW Solutions Stat 102 - 67917 X 1 − 53750 X 2 37083 X 3...

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X ijk 1 = 1 if experimental unit from row blocking class 1 1 if experimental unit from row blocking class 4 0 otherwise X ijk 2 and X ijk 3 are deFned similarly X ijk 4 = 1 if experimental unit from column blocking class 1 1 if experimental unit from column blocking class 4 0 otherwise X ijk 5 and X ijk 6 are deFned similarly X ijk 7 = 1 if experimental unit received treatment 1 1 if experimental unit received treatment 4 0 otherwise X ijk 8 and X ijk 9 are deFned similarly b. ±ull model : ˆ Y =2 . 05625 . 70625 X 1 . 45625 X 2 + . 34375 X 3 + . 14375 X 4 . 05625 X 5 . 00625 X 6 . 33125 X 7 . 15625 X 8 + . 11875 X 9 SSE ( F )= . 1188 Reduced model : ˆ Y =2 . 05625 . 70625 X 1 . 45625 X 2 + . 34375 X 3 + . 14375 X 4 . 05625 X 5 . 00625 X 6 SSE ( R )=1 . 2556 H 0 : all τ k equal zero ( k =1 , 2 , 3), H a : not all τ k equal zero. F =(1 . 1368 / 3) ÷ ( . 1188 / 6)=19 . 138, F ( . 95; 3 , 6)=4 . 76 . If F 4 . 76 conclude H 0 , otherwise H a . Conclude H a . c. ˆ L τ 3 ( ˆ τ 1 ˆ τ 2 ˆ τ 3 )=2ˆ τ 3 τ 1 τ 2 = . 250, s 2 { ˆ τ i } = . 00371 ( i =1 , 2 , 3), s { ˆ τ 1 , ˆ τ 2 } = s { ˆ τ 1 , ˆ τ 3 } = s { ˆ τ 2 , ˆ τ 3 } = . 00124 ,s { ˆ L } = . 09930, t ( . 975; 6) = 2 . 447, . 250 ± 2 . 447( . 09930) , . 493 L ≤− . 007 d. (i) ±ull model : ˆ Y =2 . 02917
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Unformatted text preview: . 67917 X 1 − . 53750 X 2 + . 37083 X 3 + . 17083 X 4 − . 02917 X 5 − . 08750 X 6 − . 30417 X 7 − . 23750 X 8 + . 14583 X 9 SSE ( F ) = . 0483 Reduced model : ˆ Y = 2 . 05556 − . 70556 X 1 − . 45833 X 2 + . 34444 X 3 + . 14444 X 4 − . 05556 X 5 − . 00833 X 6 SSE ( R ) = 1 . 2556 H : all τ k equal zero ( k = 1 , 2 , 3), H a : not all τ k equal zero. F ∗ = (1 . 2073 / 3) ÷ ( . 0483 / 5) = 41 . 66, F ( . 95; 3 , 5) = 5 . 41. If F ∗ ≤ 5 . 41 conclude H , otherwise H a . Conclude H a . (ii) ˆ L = ˆ τ 1 − ˆ τ 2 = − . 06667, s 2 { ˆ τ 1 } = . 00191, s 2 { ˆ τ 2 } = . 00272 , s { ˆ τ 1 , ˆ τ 2 } = − . 00091, s { ˆ L } = . 0803, t ( . 975; 5) = 2 . 571 , − . 06667 ± 2 . 571( . 0803), − . 273 ≤ L ≤ . 140 28-3...
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