Exam1Solutions - IE 410 Midterm Exam Answers Fall 2003...

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Unformatted text preview: IE 410 Midterm Exam Answers Fall 2003 Average = 78.4 90 | 7 5 3 2 2 1 1 80 | 9 8 8 6 6 6 5 5 3 0 70 | 9 9 9 6 5 5 60 | 4 4 2 0 50 | 2 40 | 3 30 | 7 Question 1 An experiment will be conducted to see if the priced offered by car dealers for a used car varies with the characteristics of the seller of the car. Four sellers (A, B, C, D) will be selected to solicit offers from various used car dealers. Owners A and D are male while B and C are female. Owners A and C are in their 40s while B and D are over 65 years of age. A single used car will be taken to several different dealers. Each owner will take the car to several dealers and received a cash offer. The resulting data will be recorded in units of hundreds of dollars. Suppose based on prior information, you guess that the variance 2 is about 3.0 (note the units are hundreds of dollars). You would like to detect a difference in means of $400 with probability 0.05. You will conduct your anova at =0.05. What sample size would you recommend? We will need to be careful with our units here. n n Thus dollars of units use we If n n Thus units in Then units in If of units use will we First a n D a nD 8165 . ) 4 ( 2 2 . 173 400 2 . 173 8165 . ) 4 ( 2 732 . 1 4 100 $ 732 . 1 3 100 $ . 3 100 $ 2 2 2 2 2 2 2 = = = = = = = = = = The following calculation would be incorrect: 2 = nD 2 /2a 2 = n(400) 2 /(2*4*300) = 66.67n = 8.165 n n v 1 =a-1 v 2 =a(n-1) 6 3 20 2 0.15 8 3 28 2.309401 0.05 9 3 32 2.44949 0.02 Thus n is in the range 8 or 9 and N is 32 to 36. Question 2 Despite your recommendation in question 1, the experiment was run, and the data below observed (again in units of hundreds of dollars) Owner A B C D-------------------------------- 25 21 26 20 24 25 29 23 26 23 27 24 27 22 28 26 23 20 29 21 28 22 28 23 a) Construct the ANOVA table and conduct the ANOVA F-test. Do not consider residual analysis in question 2 (we will do this in question 3). Even if the residuals indicate model inadequacy, pretend as if the model is adequate. . ANOVA Table for Y by Factor Analysis of Variance----------------------------------------------------------------------------- Source Sum of Squares Df Mean Square F-Ratio P-Value----------------------------------------------------------------------------- Between groups 121.833 3 40.6111 13.10 0.0001 Within groups 62.0 20 3.1----------------------------------------------------------------------------- Total (Corr.) 183.833 23 What is the P-value of the ANOVA F-test? ___0.0001____ b) What contrast would you recommend to test for differences in cash offers between sexes? L sex = A + D- B- C The answer age is wrong, and makes no sense since I clearly said that I was interested in looking at differences between the sexes. c) Estimate the contrast in part b) and provide a 99% confidence interval....
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This note was uploaded on 08/06/2008 for the course IE 410 taught by Professor Storer during the Fall '04 term at Lehigh University .

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Exam1Solutions - IE 410 Midterm Exam Answers Fall 2003...

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