HW Solutions Stat 89

HW Solutions Stat 89 - d. H0 : all j equal zero (j = 1, 2,...

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d. H 0 : all β j equal zero ( j =1 , 2 , 3), H a : not all β j equal zero. F =14 . 156 / 303 . 822 = . 047, F ( . 99; 2 , 4)=18 . 0. If F 18 . 0 conclude H 0 , otherwise H a . Conclude H 0 . e. ¯ Y . 1 . =5 6 . 133, ¯ Y . 2 . =5 6 . 600, ¯ Y . 3 . =5 4 . 733, ˆ D 1 = ¯ Y . 1 . ¯ Y . 2. = . 467, ˆ D 2 = ¯ Y . 1 . ¯ Y . 3 . = 1 . 400, ˆ D 3 = ¯ Y . 2 . ¯ Y . 3 . =1 . 867, s { ˆ D i } =6 . 3647 ( i =1 , 2 , 3), q ( . 95; 3 , 4)=5 . 04, T =3 . 5638 . 467 ± 3 . 5638(6 . 3647) 23 . 150 D 1 22 . 216 1 . 400 ± 3 . 5638(6 . 3647) 24 . 083 D 2 21 . 283 1 . 867 ± 3 . 5638(6 . 3647) 20 . 816 D 3 24 . 550 f. ˆ µ . 1 =56 . 1333, MSA =12 . 28889, MSAB = 303 . 82222, s 2 { ˆ µ . 1 } =(2 / 45)(303 . 82222)+ (1 / 45)(12 . 28889) = 13 . 7763, s { ˆ u . 1 } =3 . 712, df = (13 . 7763) 2 ÷{ [(2 / 45)(303 . 82222)] 2 / 4+ [(1 / 45)(12 . 28889)] 2 / 2 } =4 . 16, t ( . 995; 4) = 4 . 60, 56 . 1333 ±
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