hw problem set 1

hw problem set 1 - A Zaeske ECON 41 Homework 1 Answer...

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A. Zaeske ECON 41 Homework 1: Answer Key (Corrected) 1A : (c) 1B : (c) 1C : (a) 1D : (d) 2 : (c) 3 : (d) 4 : (d) 5 : (b) 6A : (d) 6B : (c) 3.13 : a) mean=¯ x = 1 n x = 1128 . 92 thousand employees Ordering the data in ascending order, the 25th and 26th values are 739 and 759. We average them to obtain the median. So median = 739+759 2 = 749 thousand employees b) The mode is 1200, which occurs three times. 3.25 : Using the given formula and the hint, combined mean= ¯ x = 10 * 95+8 * 104 10+8 = 99 3.28 : The mean ¯ x = 1 n x = $79 , 520, so x = n ¯ x = 5 * $79 , 520 = $397 , 600 3.39 : The standard deviation is zero when each value of the data set is the same. Let n = 4 and X = { 5 , 5 , 5 , 5 } . x = 20, x 2 = 100, s 2 = 1 3 ( 100 - 1 4 (20) 2 ) 2 = 0. So s = 0 as well. 3.46 : Range 236.7-51.6 = 185.1, x = 1147 . 30, x 2 = 169226 . 29 Sample Values : s 2 = 1 9 ( 169226 . 29 - 1 10 (1147 . 30) 2 ) 2 = 4177 . 4 s = 64 . 63 Population Values : σ 2 = 1 10 ( 169226 . 29 - 1 10 (1147 . 30) 2 ) 2 = 3759 . 66 σ = 61 . 32 3.57 : Salary - CV = σ μ = $6 , 820 $62 , 350 * 100 = 10 . 94% Years of Experience - CV= σ μ = 2 15 * 100 = 13 . 33% The relative variation is greater in years of experience than in salaries. 3.81 : a) i) This range is 2s away from ¯ x . So by Chebyshev’s Theorem, 1 - 1 2 2 = . 75 or 75% ii) This range is 3s away from ¯ x . So by Chebyshev’s Theorem, 1 - 1 3 2 = 8 9 = . 8889 or 88
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