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HW Solutions Stat 58

HW Solutions Stat 58 - b 18.17 a Y1 =.08 Y2 =.12 Y3 =.47 Y4...

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b. ˜ Y 1 = . 08, ˜ Y 2 = . 12, ˜ Y 3 = . 47, ˜ Y 4 = . 41, ˜ Y 5 = . 175, ˜ Y 6 = . 125, MSTR = . 002336, MSE = . 012336, F L = . 002336 /. 012336 = . 19, F ( . 99; 5 , 114) = 3 . 18. If F L 3 . 18 conclude H 0 , otherwise H a . Conclude H 0 . P -value = . 97 18.17. a. ¯ Y 1 . = 3 . 5625, ¯ Y 2 . = 5 . 8750, ¯ Y 3 . = 10 . 6875, ¯ Y 4 . = 15 . 5625 e ij : i j = 1 j = 2 j = 3 j = 4 j = 5 j = 6 1 . 4375 . 5625 1 . 5625 . 5625 . 4375 . 4375 2 1 . 1250 . 1250 1 . 8750 . 1250 1 . 1250 3 . 8750 3 1 . 3125 4 . 6875 3 . 3125 1 . 3125 . 6875 1 . 6875 4 . 4375 1 . 5625 9 . 5625 3 . 4375 3 . 5625 5 . 5625 i j = 7 j = 8 j = 9 j = 10 j = 11 j = 12 1 . 5625 2 . 4375 1 . 4375 . 4375 1 . 5625 . 4375 2 3 . 1250 . 8750 . 8750 3 . 1250 2 . 8750 2 . 1250 3 1 . 3125 6 . 3125 3 . 6875 4 . 6875 1 . 3125 . 3125 4 . 5625 8 . 4375 5 . 5625 7 . 4375 1 . 4375 4 . 4375 i j = 13 j = 14 j = 15 j = 16 1 . 4375 1 . 5625 . 5625 . 4375 2 . 1250 1 . 8750 1 . 1250 . 1250 3 4 . 6875 2 . 3125 . 6875 3 . 3125 4 . 5625 2 . 4375 7 . 5625 6 . 4375 c. H 0 : all σ 2 i are equal ( i = 1 , 2 , 3 , 4), H a : not all σ 2 i are equal. ˜ Y 1 = 4 . 0, ˜ Y 2 = 6 . 0, ˜ Y 3 = 11 . 5, ˜ Y 4 = 16 . 5, MSTR = 37 . 1823, MSE = 3 . 8969, F L = 37 . 1823 / 3 . 8969 = 9 . 54, F
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