2010-2 STAT FALL midterm _1 q

2010-2 STAT FALL midterm _1 q - Dr. V.R. Bencivenga...

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Dr. V.R. Bencivenga September 29, 2010 Economics 329 Fall 2010 MIDTERM EXAM #1 Instructions: Answer the questions below in a blue book. The exam consists of ten questions worth a total of 200 points. The exam will last two hours. This is an open book, open notes exam. Show your work to receive credit. Good luck! (20 points) 1. Below are two relative frequency distributions of ages of heads of households in the U.S. in 1988. The first includes all households , and the second includes only poor households (households below the poverty line). Age of head % of all % of poor of household households households 15 to < 25 5.7 13.0 25 to < 35 22.6 33.0 35 to < 45 21.2 21.8 45 to < 55 15.0 11.3 55 to < 65 14.1 10.7 65 and over 21.4 10.2 a. What is the median age of the head of a poor household? b. Without calculating it , say whether the median age of the head of a household (based on all households ) is smaller or larger than that of a poor household. Briefly explain how you know. (15 points) 2. Suppose we have a sample of 100 small airports. We have data on the number of airlines and price per passenger mile. In the data , the number of airlines serving each airport is 2, 3, 4, or 5. Also, in the data , price per passenger mile on routes from these airports is $.15, $.20, or $.25. Below are relative frequencies in the data . For example, .1 of the airports in the sample or 10 observations out of 100 have 4 airlines and price per passenger mile equal to .15 dollars, and so forth. X = NUMBER OF AIRLINES 2 3 4 5 .15 0 0 .1 .2 Y = PASSENGER MILES ($) .20 .1 .1 .1 .1 .25 .2 .1 0 0 a. What is the sample mean price per passenger mile? b. What is the sample variance of price per passenger mile? c. Without doing the calculations , give an expression for the covariance between number of airlines and price per passenger mile (using the numbers in this problem). Give the units of the covariance.
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2 (30 points) 3. (continued) Now interpret these relative frequencies as probabilities. X = NUMBER OF AIRLINES 2 3 4 5 .15 0 0 .1 .2 Y = PASSENGER MILES ($) .20 .1 .1 .1 .1 .25 .2 .1 0 0 What is the probability that a randomly-chosen airport a. has 2 airlines and price per passenger mile equal to .20? b. has price per passenger mile equal to .20?
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2010-2 STAT FALL midterm _1 q - Dr. V.R. Bencivenga...

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