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AK2_230

# AK2_230 - ECO 230 Economic Statistics Answer Key to...

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ECO 230 Marianna Kudlyak Economic Statistics Spring 2007 Answer Key to Homework #2 Total points: 10. Graded exercises: Ex.1 (2 points), Ex.4 (2 points), Ex. 6 (2 points), and Ex. 7 (2 points). 0.5 points were added for the presence of each of the remaining 4 exercises. Exercise 1. A survey of 12 students at a local university asked approximately how many hours per week they spend on the Internet. Their answers are listed below. 1 3 0 5 8 2 2730 1 51 2 1 3 1 6 a) What are the mean and median for this data? Using the formula for sample mean: mean is 9.5 To obtain a median, order the data in ascending order: 0 0 3 5 7 8 12 13 13 15 16 22 Median is 8+(1/2)*(12-8) = 8+2=10 b) From the data presented above, calculate the first and third quartiles. 1 st quartile: (1/4)*(n+1)th observation = 3.25th observation = 3+(1/4)*(5-3) = 3+2/4=3.5 3 rd quartile: (3/4)*(n+1)th observation = 9.75th observation = 13+(3/4)*(15-13) = 13+(6/4) = 14.5 c) From the data presented above calculate the inter-quartile range. 3 rd quartile - 1 st quartile = 14.5-3.5 = 11 d) What is the coefficient of variation for this data? Using the value of the standard deviation from part e) below, CV = = x s 6.82/9.5 = 0.72 or 72% e) What is the variance and the standard deviation for this data? Using the formulas for sample standard deviation and sample variance: s 2 = = = 1 12 ) ( 12 1 2 i i x x 46.45 s = 6.82 f) What is the range of this data? Range is Max – Min = 22-0=22 Exercise 2. Inflation rates in small country for the past five years have been 10%, 7%, 13%, 9%, and 12%. a) What is the average annual rate of inflation? Use the geometric mean to calculate the mean inflation rates: {(10)(7)(13)(9)(12)] 1/5 = 9.96536 b) If this rate of inflation continues, how long will it take for prices to double?

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Number of years for the inflation to double at this growth rate: Solve the following equation for x: (1.0996536) X = 2.0. Take the log of both sides of the equation: X log(1.0996536) = log (2.0). Simplify: X = .301029996/.0412559 = 7.297 years Exercise 3. Newbold, Carlson and Thorne, Problem 3.31 p.64.
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AK2_230 - ECO 230 Economic Statistics Answer Key to...

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