Quiz_1_Solutions

Quiz_1_Solutions - n-1 S 2 2,n-1 = 8 144 15 507 =(94 56...

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IEOR 165: Engineering Statistics, Quality Control and Forecasting, Spring 2007 Quiz 1 Solution Question 1 (a) Noting ¯ x = 102, S 2 = 144, the 95 percent CI for the mean is ¯ x ± t α/ 2 ,n - 1 S n = 102 ± 2 . 306 12 3 ! = (92 . 776 , 111 . 224) . The 95 percent CI for the variance is ( n - 1) S 2 χ 2 α/ 2 .n - 1 , ( n - 1) S 2 χ 2 1 - α/ 2 ,n - 1 = 8 · 144 17 . 535 , 8 · 144 2 . 180 ! = (65 . 7 , 528 . 44) . (b) The 95 percent upper CI for the mean is x - t α,n - 1 S n , ) = (102 - 1 . 85 · 4 , ) = (94 . 56 , ) . The 95 percent upper CI for the variance is
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Unformatted text preview: ( n-1) S 2 2 ,n-1 , = 8 144 15 . 507 , ! = (94 . 56 , ) . Question 2 Noting that x = 102, = 11, the 95 percent CI for the mean is x Z / 2 n = 102 1 . 96 11 3 ! = (94 . 813 , 109 . 19) . The 95 percent CI for the variance is (121 , 121). Question 3 (a) True (b) False (c) False (d) True 1...
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