Assignment 11 solutions - Fall 2009 Hansen Assignment 11...

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Unformatted text preview: Fall 2009 Hansen Assignment 11 solutions Due 11/24/2009 9:10 AM 1. Problem 7.9 in Ross. ~ 0, , = 0.08, a) − 1.96 , + 1.96 b) −∞, + 1.645 − 1.645 c) = 10, = 11.48 = 11.48 − 1.96 , ∞ = 11.44, ∞ Confidence interval for : − ,+ , = 24, = 333.996, b) . = 11.43, 11.53 = 0,11.52 PCB concentration in fish can’t be less than zero. 2. Problem 7.17 in Ross. unknown; use t-distribution a) , 11.48 + 1.96 . = = 0.05, . , = 2.069 2-sided 95% CI: 331.06, 336.93 , 1 −1 − = 6.9576 = 0.01, . , = 2.807 2-sided 99% CI: 330, 338 3. Problem 7.20 in Ross. = 16, = 2200, = 800 We want 2-sided 90% CI for 2200 − 1.753 ∗ , = . , = 1.753 800 800 , 2200 + 1.753 ∗ = 1849.4, 2550.6 4 4 4. Problem 7.41 in Ross. = = 10 = 3358.1, = 3130.4 = 352.7311, = 133.1492 = = 0.10 = 71073.955 Fall 2009 Hansen a) 2-sided 95% confidence interval = 0.05, . , = 2.101 − ± ∗ , b) Upper 1-sided 95% confidence interval = 1.734 ., 20.96, ∞ c) Lower 1-sided 95% confidence interval −∞, 434.44 1 + 1 = −22.8,478.19 5. Problem 7.50 in Ross. Formula from Ross, page 266: 1− = We know that we must collect at least samples according to the formula above. However, before we start collecting samples we have no idea what is going to be. Therefore, what we can do is simply make sure that we collect as large as is necessary, which it will be if 1 − is as large as possible. If = 1− Find = 1 − 2 = 0 such that = 0.5 (where 0 ≤ And then the largest sample we need to collect will be From the question we know = 0.10 = 1.645 and = 0.02 ∗ 2 . And = 1.645 = 1691 0.04 ≤1 = ∗= ...
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