statsexam3f06sol

statsexam3f06sol - Economic Statistics Exam 3 December 12,...

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Economic Statistics Exam 3 Last name: December 12, 2006 First name: PPID: Please sign that you abide by the honor pledge: This exam contains twenty short answer questions ( worth 4 points each ) and six long answer questions ( worth 15 points each ) . Please answer in the space provided; if you need more room, indicate clearly that the answer is continued on the back of the page. In all problems where you need to make a calculation, simplify your answer as much as possible. Show your work clearly to be eligible for partial credit. Some PDFs: Some probabilities: f ( x ) = 1 2 !" 2 e # ( X # μ ) 2 " 2 P [ x ! a ] = e " # a f ( x ) = 1 u ! ! P [ X ] = x e ! X ! f ( x ) = ! e " x P [ X ] = N ! X !( N ! X )! p X (1 ! p ) N ! X Short Questions ( 4 points apiece ) 1. You have a small stock portfolio. Over the past year, the returns on these stocks were: - 28 % , - 6 % , - 3 % , 1 % , 1 % , 5 % , 12 % , 28 % , and 43 % . Give the five - number summary of this distribution. Max: 43 % 75 th : 12 % Median: 1 % 25 th : - 3 % Min: - 28 % 2. In general, I believe that pie charts are uninformative ( or rather, that they are no more informative than a list of proportions ) . However, I did name one “good” way to use pie charts. What is it? When placed side - by - side, so that we can easily compare proportions in different groups.
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3. A database contains the fuel efficiency ( in terms of miles per gallon ) of seventeen car models. These values are: 18.6 19.9 20.5 32.8 19.2 20.2 20.6 36.1 19.4 20.2 20.8 36.1 19.4 20.5 25.1 39.4 43.1 Construct a box - and - whisker plot to describe this data. The box goes from 19.9 ( the 25 th percentile ) to 32.8 ( the 75 th percentile ) , with a vertical line at 20.5 ( the median ) . The whiskers extend to 18.6 and 43.1. 4. The starting salaries of economics majors are distributed with a mean of $ 35,000 and a standard deviation of $ 5,000. With this information ( and no additional assumptions! ) , calculate the fraction of salaries between $ 25,000 and $ 45,000. According to Chebyshev’s Theorem, at least ( 1 ! 1 k 2 ) fraction of observations lie within k standard deviations of the mean. In this problem, $ 25,000 is two standard deviations below the mean and $ 45,000 is two standard deviations above, so at least ( 1 ! 1 2 2 ) = 3 4 of observations are within this range. 5. On any given day, it can be sunny or rainy, and it can be cold or warm. There is a 0.30 chance that it is rainy; there is a 0.20 chance that it is cold; and there is a 0.25 chance that it is both rainy and cold. What is the probability that it is cold or rainy ( or both ) ? P [cold or rain] = P [cold] + P [rain] ! P [cold and rain] = 0 . 30 + 0 . 20 ! 0 . 25 = 0 . 25 ( As a note, the probabilities in the problem are impossible. Oops. ) 6. The Center for Disease Control estimates that about 1 in 300 Americans is infected with HIV. There is a rapid test for HIV, which is fairly accurate. Among people with the virus, 99 of 100 tests are positive; among people without the virus, 1 out of 200 tests results in a ( false ) positive. If someone takes the test and gets a positive result, what is the chance that he is infected with the virus?
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statsexam3f06sol - Economic Statistics Exam 3 December 12,...

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