EC351_Test1_Sample_Answers

EC351_Test1_Sample_Answers - Test 1 Review Questions EC 351...

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Test 1 Review Questions EC 351 Hammond 1. Math SAT scores are distributed normally with (500,10000) N . (a) What fraction of students scores above 750? Above 600? Between 420 and 530? Below 480? Above 530? Answer: Pr(Y>750) = 0.0062; Pr(Y>600) = 0.1587; Pr(420<Y<530) = 0.4060; Pr(Y<480) = 0.4270; Pr(Y>530) = 0.3821. (b) Assume that you had chosen 25 students at random who had taken the SAT exam. Derive the distribution for their average math SAT score. What is the probability that this average is above 530? Why is this so much smaller than your answer in (a)? Answer: The distribution for the average math SAT score is (500,400) N . Pr( 530) Y = 0.0668. This probability is smaller because the sample mean has a smaller standard deviation (20 rather than 100). (c) Verbal SAT scores are also distributed normally with (500,10000) N . If the math and verbal scores were independently distributed (which is not a realistic assumption) then what would be the distribution of the overall SAT score? Find its mean and variance. Answer: The distribution would be (1000,20000) N , using equations (2.29) and (2.31) in the textbook. Note that the standard deviation is now roughly 141 rather than 200. (d) Next, assume that the correlation coefficient between the math and verbal scores is 0.75. Find the mean and variance of the resulting distribution. Answer: Given the correlation coefficient, the distribution is now (1000,35000) N , which has a standard deviation of approximately 187.
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2. Following Alfred Nobel’s will, there are five Nobel Prizes awarded each year. These are for outstanding achievements in Chemistry, Physics, Physiology or Medicine, Literature, and Peace. In 1968, the Bank of Sweden added a prize in Economic Sciences in memory of Alfred Nobel. The accompanying table lists the joint probability distribution between recipients in economics and the other five prizes, and the citizenship of the recipients, based on the 1969-2001 period. Joint Distribution of Nobel Prize Winners in Economics and Non-Economics Disciplines, and Citizenship, 1969-2001 U.S. Citizen ( 0 Y ) Non-U.S. Citizen ( 1 Y ) Total Economics Nobel Prize ( 0 X ) 0.118 0.049 0.167 Physics, Chemistry, Medicine, Literature, and Peace Nobel Prize ( 1 X ) 0.345 0.488 0.833 Total 0.463 0.537 1.00 (a) Compute () E Y . Answer: () 0 . 5 3 7 EY . 53.7 percent of Nobel Prize winners were non-U.S. citizens. (b) Calculate (| 1 ) EY X and 0 ) . Answer: ( | 1) 0.586  . 58.6 percent of Nobel Prize winners in non-economics disciplines were non-U.S. citizens. ( | 0) 0.293 . 29.3 percent of the Economics Nobel Prize winners were non-U.S. citizens. (c) A randomly selected Nobel Prize winner reports that he is a non-U.S. citizen. What is the probability that this genius has won the Economics Nobel Prize? A Nobel Prize in the other five disciplines? Answer: There is a 9.1 percent chance that he has won the Economics Nobel Prize, and a 90.9 percent chance that he has won a Nobel Prize in one of the other five disciplines.
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3. The expectations augmented Phillips curve postulates () pf u u  , where p is the actual inflation rate, is the expected inflation rate, and u is the unemployment rate, with “–” indicating equilibrium (the NAIRU – Non-Accelerating Inflation Rate of Unemployment). The accompanying table below displays information on accelerating
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This note was uploaded on 09/18/2011 for the course ECON 351 taught by Professor Hammond during the Fall '10 term at N.C. State.

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EC351_Test1_Sample_Answers - Test 1 Review Questions EC 351...

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