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s04pre1

# s04pre1 - Prof G Jakubson Economics 321 Spring 2004...

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Prof. G. Jakubson Economics 321 March 2004 Spring 2004 PRELIMINARY EXAM #1 This is a closed book exam. You are permitted to have a calculator. There is a formula sheet at the end of the exam (Appendix 2), and some empirical results that you will need to refer to in Appendix 1. Answer the questions below in an exam book or books. SHOW YOUR WORK ! Be sure to label each answer, and each part of each answer, clearly. Neatness counts -- if I cannot read it I cannot give you credit. If you get stuck on a particular problem, skip it and move on to the next one. If you cannot remember exactly how to answer a question, you may get partial credit for setting it up even if you don't solve it. As it says on the cover of The Hitchhiker's Guide to the Galaxy , DON'T PANIC ! Note that questions have different weights, and parts within a question may not be weighted equally. If you get stuck on a particular problem, skip it and move on to the next one. If you cannot remember exactly how to answer a question, you may get partial credit for setting it up even if you don't solve it. Read the questions carefully. You have 75 minutes to complete the nine (9) questions on the exam. 1. (20 points) Below are the frequency distributions of family incomes in 1988, for Caucasian families and African-American families. These data are adapted from the U.S. Bureau of the Census. Class intervals thousands of families for family income Caucasian African-American < \$5,000 2,000 900 \$ 5,000 to < \$10,000 3,000 1,100 \$10,000 to < \$15,000 5,000 900 \$15,000 to < \$25,000 10,000 1,600 \$25,000 to < \$35,000 10,000 900 \$35,000 to < \$50,000 12,000 900 14,000 600 \$50,000 or more Total number of families 56,000 6,900 a. In what class interval is median family income of African-American families? Which distribution has the higher median family income? (You do not need to calculate median family income for Caucasian families, but you should explain how you can tell which distribution has a higher median.) b. Give the cumulative relative frequency distribution of family income of African-American families. 2. (25 points) Suppose you have data on a variable X. A "standardized" variable Z is constructed by using the following linear transformation: x i i s / ) x x ( z = for each observation i = 1, . .., n. a. What is Z ? b. What is s z ? Economics 321, Cornell University Page 1 of 6 Prelim 1, Spring 2004 c:\…\s04pre1.doc

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Now suppose that you measure a linear transformation of X, namely Y i = d 1 + d 2 X i for some values of d 1 and d 2 , and you construct a standardized measure of Y using T i = (Y i - Y ) / s y .
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s04pre1 - Prof G Jakubson Economics 321 Spring 2004...

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