HW Solutions Stat 79

# HW Solutions Stat 79 - H0 1 = 2 = 0 Ha not both 1 and 2...

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H 0 : α 1 = α 2 =0 , H a : not both α 1 and α 2 equal zero. F = (288 . 6061 / 2) ÷ (71 . 3333 / 28)=56 . 64, F ( . 95; 2 , 28)=3 . 34. If F 3 . 34 conclude H 0 , otherwise H a . Conclude H a . P -value = 0+ B eFects : ˆ Y =23 . 56667 2 . 06667 X 1 +4 . 13229 X 2 . 17708 X 1 X 3 . 31146 X 2 X 3 , SSE ( R )=75 . 8708 H 0 : β 1 =0 , H a : β 1 6 =0 . F =(4 . 5375 / 1) ÷ (71 . 3333 / 28)=1 . 78, F ( . 95; 1 , 28)=4 . 20. If F 4 . 20 conclude H 0 , otherwise H a . Conclude H 0 . P -value = . 19 g. ˆ D 1 α 1 ˆ α 2 = 6 . 23334, ˆ D 2 α 1 ˆ α 3 =2ˆ α 1 α 2 = . 03333 , ˆ D 3 α 2 ˆ α 3 = α 2 α 1 =6 . 26667, s 2 { ˆ α 1 } = . 14625, s 2 { ˆ α 2 } = . 15333, s { ˆ α 1 , ˆ α 2 } = . 07313, s { ˆ D 1 } = . 6677, s { ˆ D 2 } = . 6677, s { ˆ D 3 } = . 6834, q ( . 90; 3 , 28)=3 . 026, T =2 . 140 6 . 23334 ± 2 . 140( . 6677) 7 . 662 D 1 ≤− 4 . 804 . 03333 ± 2 . 140( . 6677) 1 . 396 D 2 1 . 462 6 . 26667 ± 2 . 140( . 6834) 4 . 804 D 3 7 . 729 h. ˆ L = . 3 ¯ Y 12 . + . 6 ¯ Y 22 . + . 1 ¯ Y 32 . = . 3(21 . 33333)+ . 6(27 . 66667)+ . 1(20 . 60000) = 25 . 06000, s { ˆ L } = . 4429, t ( . 975; 28) = 2 . 048 , 25 . 06000 ± 2 . 048( . 4429), 24 . 153 L 25 . 967 23.7. a. Y ijk = µ .. + α i + β j +( αβ ) ij + ± ijk Y ijk = µ .. + α 1 X ijk 1 + α 2 X ijk 2 + β 1 X ijk 3 + β 2 X ijk 4 +( αβ ) 11 X ijk 1 X ijk 3 +( αβ ) 12 X ijk 1 X ijk 4
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