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ieor_hw2_sol

# ieor_hw2_sol - IEOR 165 Engineering Statistics Quality...

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IEOR 165: Engineering Statistics, Quality Control and Forecasting, Spring 2008 Homework 2 Solution Chapter 7 Question 8 Noting ¯ X = 3 . 1502 (a) 95 percent CI: ¯ X ± 1 . 96 σ n = 3 . 1502 ± 1 . 96( . 1) / 5 = (3 . 0625 , 3 . 2379) (b) 99 percent CI: ¯ X ± z . 005 σ n = 3 . 1502 ± 12 . 58( . 1) / 5 = (3 . 0348 , 3 . 2656) Question 13 99 percent CI: ¯ X ± z . 005 σ n = 1 . 2 ± z . 005 0 . 2 / 20 = (1 . 0848 , 1 . 3152) Question 14 99 percent CI: ¯ X ± t . 005 ,n - 1 S n = 1 . 2 ± t . 005 , 19 0 . 2 / 20 = (1 . 0720 , 1 . 3280) Question 17 Using the two-sided CI on mean with unknown variance ¯ X ± t α/ 2 ,n - 1 S n (a) 95 percent CI: (331.0572,336.9345) (b) 99 percent CI: (330.0082,337.9836) Question 18 Noting ¯ X = 133 . 22, S = 10 . 2127 (a) 95 percent CI: ¯ X ± t . 025 ,n - 1 S n = (128 . 14 , 138 . 30) (b) 95 percent lower CI: ( -∞ , ¯ X + t . 05 ,n - 1 S n ) = ( -∞ , 137 . 41) (c) 95 percent upper CI: ( ¯ X - t . 05 ,n - 1 S n , ) = (129 . 03 , ) Question 22 (a) 95 percent CI: ¯ X ± t . 025 ,n - 1 S n = 330 . 2 ± 2 . 094(15
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