HW Solutions Stat 81

HW Solutions Stat 81 - 2.0542 3.9395.1613 3.5625...

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2 . 0542 ± 3 . 9395( . 1613) 1 . 419 L 1 2 . 690 3 . 5625 ± 3 . 9395( . 1695) 2 . 895 L 2 4 . 230 5 . 7875 ± 3 . 9395( . 1570) 5 . 169 L 3 6 . 406 1 . 5083 ± 3 . 9395( . 2340) . 586 L 4 2 . 430 3 . 7333 ± 3 . 9395( . 2251) 2 . 846 L 5 4 . 620 2 . 2250 ± 3 . 9395( . 2310) 1 . 315 L 6 3 . 135 23.12. a. See Problem 19.14a. ˆ D 1 = ¯ Y 13 . ¯ Y 11 . = 2 . 100, ˆ D 2 = ¯ Y 23 . ¯ Y 21 . = 3 . 675, ˆ D 3 = ¯ Y 33 . ¯ Y 31 . = 7 . 275, ˆ L 1 = ˆ D 1 ˆ D 2 = 1 . 575, ˆ L 2 = ˆ D 1 ˆ D 3 = 5 . 175, MSE = . 06406, s { ˆ D i } = . 1790 ( i = 1 , 2 , 3), s { ˆ L i } = . 2531 ( i = 1 , 2), B = t ( . 99; 24) = 2 . 492 2 . 100 ± 2 . 492( . 1790) 1 . 654 D 1 2 . 546 3 . 675 ± 2 . 492( . 1790) 3 . 229 D 2 4 . 121 7 . 275 ± 2 . 492( . 1790) 6 . 829 D 3 7 . 721 1 . 575 ± 2 . 492( . 2531) 2 . 206 L 1 ≤ − . 944 5 . 175 ± 2 . 492( . 2531) 5 . 806 L 2 ≤ − 4 . 544 b. H 0 : µ 12 µ 13 = 0, H a : µ 12 µ 13 = 0. ˆ D = ¯ Y 12 . ¯ Y 13 . = . 025, s { ˆ D } = . 1790, t = . 025 /. 1790 = . 14, t ( . 99; 24) = 2 . 492. If | t | ≤ 2 . 492 conclude H 0 , otherwise H a . Conclude H 0 . H 0 : µ 32 µ 33 = 0, H a : µ 32 µ 33 = 0. ˆ D = ¯ Y 32 . ¯ Y 33 . = 2 . 975, s { ˆ D } = . 1790, t = 2 . 975 /. 1790 = 16 . 62, t ( . 99; 24) = 2 . 492. If | t | ≤ 2 . 492 conclude H 0 , otherwise H a . Conclude H a . α . 04 23.14. a. See Problem 19.20a. ˆ D 1 = ¯ Y 12 . ¯ Y 13 . = 46 . 0, ˆ D 2 = ¯ Y 22 . ¯ Y 23 . = 6 . 0, ˆ L 1 = ˆ D 1 ˆ D 2 = 40 . 0, MSE = 88 . 50, s { ˆ D 1 } = s { ˆ D 2 } = 6 . 652, s { ˆ L 1 } = 9 . 407, B = t ( . 99167; 15) = 2
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