CEE3770_Sum09_HW3_solns

CEE3770_Sum09_HW3_solns - CEE 3770 - Summer 2009 Homework 3...

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CEE 3770 - Summer 2009 Homework 3 (due on 06/18) 1. An apparel and shoe trade association has 8,900 member firms. As a part of a study of the impact of new minimum-wage legislation on association members, a random sample of 400 member firms was selected to estimate μ , the mean number of hourly-paid employees in member firms. A computer analysis of the sample results showed: X = 8 . 31, where X denotes the number of hourly paid employees in a firm. Suppose that you know that X is normal distributed with known variance σ 2 = 4 . 16 2 . (a) Construct 94% confidence interval for μ . Solution: 94% CI = X ± z α/ 2 r σ 2 n = 8 . 31 ± z 0 . 03 r 4 . 16 2 400 = 8 . 31 ± 1 . 88 · 4 . 16 20 = 8 . 31 ± 0 . 39104 (b) If you had constructed a 99% confidence interval, would it have been wider or narrower than one in (a)? Solution: Wider. 2. The EPA standard on the amount of suspended solids discharged into rivers and streams is a maximum of 60 milligrams per liter daily, with a maximum monthly average of 30 milligrams per liter. Suppose you want to test a randomly selected sample of n water specimens and estimate the mean daily rate of pollution produced by the mining operation. If you want 95% confidence interval estimate of width 2 milligrams, how many specimens you need to sample? Assume prior knowledge indicates that pollution readings in water samples taken during a
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CEE3770_Sum09_HW3_solns - CEE 3770 - Summer 2009 Homework 3...

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