CEE3770_Sum09_PracticeTest2_solns

CEE3770_Sum09_PracticeTest2_solns - CEE 3770 - Summer 2009...

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CEE 3770 - Summer 2009 Practice Test 2 June 30, 2009 (12:00 p.m. - 1:45 p.m.) Do not read any page other than this instruction sheet before the official start time. Be sure to write your name on EVERY page! Please use the space provided to answer your questions. Use the back of each page if you need extra room. Do not attach any extra sheets. Exam is closed book. You are not allowed to use notes or textbooks. You are allowed to use a calculator, but you may not share it with anyone else. Please refer to the last pages for the standard normal distribution and t-distribution tables. 1
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Name: 1. (10 points) Suppose that b θ 1 and b θ 2 are estimators of the parameter θ . We know that E [ b θ 1 ] = θ and E [ b θ 2 ] = θ/ 2, V ar [ b θ 1 ] = 10 and V ar [ b θ 2 ] = 4. Which estimator is better? In what sense is it better? Solution: Mean Squared Error for b θ 1 = E [( θ - b θ 1 ) 2 ] = V ar ( b θ 1 ) + ( E [ b θ 1 ] - θ ) 2 = 10 + ( θ - θ ) 2 = 10 Mean Squared Error for b θ 2 = E [( θ - b θ 2 ) 2 ] = V ar ( b θ 2 ) + ( E [ b θ 2 ] - θ ) 2 = 4 + ( θ 2 - θ ) 2 = 4 + θ 2 / 4 If 4 + θ 2 / 4 < 10, i.e. θ 2 < 24, b θ 2 is a better estimator. Otherwise, b θ 1 is a better estimator. 2
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Name: 2. (18 points) A civil engineer is analyzing the compressive strength of concrete. Compressive strength is approximately normally distributed with a variance σ 2 = 1000( psi ) 2 . A random sample of 12 specimens has a mean compressive strength of X = 3250 psi. (a) Construct a 95% two-sided confidence interval on mean compressive strength. Solution: 95% CI = X ± z 0 . 025 p σ 2 /n = 3250 ± 1 . 96 p 1000 / 12 = 3250 ± 17 . 892 (b) Construct a 99% two-sided confidence interval on mean compressive strength. Compare the width of this confidence interval with the width of the one found in part (a).
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This note was uploaded on 06/29/2009 for the course CEE 3770 taught by Professor Staff during the Spring '08 term at Georgia Institute of Technology.

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CEE3770_Sum09_PracticeTest2_solns - CEE 3770 - Summer 2009...

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