HW Solutions Stat 74

HW Solutions Stat 74 - S SE (R) = 8.4889 Factor A: Yijk = ....

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SSE ( R )=8 . 4889 Factor A : Y ijk = µ .. + β 1 I ijk 3 +( αβ ) 11 I ijk 1 I ijk 3 +( αβ ) 21 I ijk 2 I ijk 3 + γx ijk + ± ijk ˆ Y =23 . 55556 + . 12982 I 3 + . 01136 I 1 I 3 + . 06818 I 2 I 3 +1 . 52893 x SSE ( R ) = 240 . 7835 Factor B : Y ijk = µ .. + α 1 I ijk 1 + α 2 I ijk 2 +( αβ ) 11 I ijk 1 I ijk 3 +( αβ ) 21 I ijk 2 I ijk 3 + γx ijk + ± ijk ˆ Y =23 . 55556 2 . 15487 I 1 +3 . 67076 I 2 . 05669 I 1 I 3 . 04071 I 2 I 3 +1 . 08348 x SSE ( R )=9 . 8393 c. H 0 :( αβ ) 11 =( αβ ) 21 =0 , H a : not both ( αβ ) 11 and ( αβ ) 21 equal zero. F =( . 1948 / 2) ÷ (8 . 2941 / 29) = . 341, F ( . 95; 2 , 29)=3 . 33. If F 3 . 33 conclude H 0 , otherwise H a . Conclude H 0 . P -value = . 714 d. H 0 : α 1 = α 2 =0 , H a : not both α 1 and α 2 equal zero. F = (232 . 4894 / 2) ÷ (8 . 2941 / 29) = 406 . 445, F ( . 95; 2 , 29)=3 . 33. If F 3 . 33 conclude H 0 , otherwise H a . Conclude H a . P -value = 0+ e. H 0 : β 1 =0 , H a : β 1 6 =0 . F =(1 . 5452 / 1) ÷ (8 . 2941 / 29)=5 . 403, F ( . 95; 1 , 29)=4 . 18. If F 4 . 18 conclude H 0 , otherwise H a . Conclude H a . P -value = . 027 f. ˆ D 1 α 1 ˆ α 2 = 5 . 83435, ˆ D 2 α 1 ˆ α 3 =2ˆ α 1 α 2 = . 62414, ˆ D 3 α 2 ˆ α 3 =2ˆ α 2 α 1 =5 . 21021, ˆ D 4 = ˆ β 1 ˆ β 2 =2 ˆ β 1 = . 41814, s 2 { ˆ α 1 } = . 01593, s 2 { ˆ α 2 } = . 01708, s { ˆ α 1 , ˆ α 2 } = . 00772, s
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