C with z 2 the empirical rule suggests that 95 of

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c. With z = 2, the empirical rule suggests that 95% of household incomes must fall between $50,789 to $115,481. For the same range, the percentage obtained using the empirical rule is greater than the percentage obtained using Chebyshev’s theorem. d. The z -score for Danbury, CT is 3.04; thus, the Danbury, CT observation is an outlier. 63. a. Public Transportation: x = = 320 10 32 Automobile: x = = 320 10 32 b. Public Transportation: s = 4.64 Automobile: s = 1.83 c. Prefer the automobile. The mean times are the same, but the auto has less variability. d. Data in ascending order: Public: 25 28 29 29 32 32 33 34 37 41 Auto: 29 30 31 31 32 32 33 33 34 35 Five number Summaries Public: 25 29 32 34 41 Auto: 29 31 32 33 35 Box Plots:
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Chapter 3 3 - 26 Public: 24 28 32 36 40 Auto: 24 28 32 36 40 The box plots do show lower variability with automobile transportation and support the conclusion in part c. 64. a. The sample covariance is 502.67. Because the sample covariance is positive, there is a positive linear relationship between income and home price. b. The sample correlation coefficient is .933; this indicates a strong linear relationship between income and home price. 65. a. Let x = media expenditures ($ millions) and y = shipments in barrels (millions) 404.1 119.9 404.1 40.41 119.9 11.99 10 10 i i x x y y Σ = = = Σ = = = 2 2 ( )( ) 3763.481 ( ) 19,248.469 ( ) 939.349 i i i i x x y y x x y y Σ = Σ = Σ = ( )( ) 3763.481 418.1646 1 10 1 i i xy x x y y s n Σ = = = A positive relationship b. 2 ( ) 19,248.469 46.2463 1 10 1 i x x x s n Σ = = = 2 ( ) 939.349 10.2163 1 10 1 i y y y s n Σ = = = 418.1646 0.885 (46.2463)(10.2163) xy xy x y s r s s = = = Note: The same value can also be obtained using Excel's CORREL function
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Descriptive Statistics: Numerical Methods 3 - 27 66. a. The scatter diagram indicates a positive relationship b. 798 11,688 1,058,019 i i i i x y x y Σ = Σ = Σ = 2 2 71,306 16,058,736 i i x y Σ = Σ = ( ) ( ) ( ) 2 2 2 2 2 2 / 1,058,019 (798)(11,688)/9 .9856 71,306 (798) /9 16,058,736 (11,688) /9 / / i i i i xy i i i i x y x y n r x x n y y n Σ − Σ Σ = = = Σ − Σ Σ − Σ Strong positive relationship 67. a. The scatter diagram is shown below: 0 0.5 1 1.5 2 2.5 3 3.5 0 5 10 15 20 25 30 Book Value Earnings b. The sample correlation coefficient is .75; this indicates a positive linear relationship between book value and earnings. 68. a. (800 + 750 + 900)/3 = 817
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Chapter 3 3 - 28 b. Month January February March Weight 1 2 3 x w x w i i i = = + + + + = = Σ Σ 1 800 2 750 3 900 1 2 3 5000 6 833 ( ) ( ) ( ) 69. 20(20) 30(12) 10(7) 15(5) 10(6) 965 11.4 20 30 10 15 10 85 i i i w x x w Σ + + + + = = = = Σ + + + + days 70. f i M i f i M i M x i ( ) M x i 2 f M x i i ( ) 2 10 47 470 -13.68 187.1424 1871.42 40 52 2080 -8.68 75.3424 3013.70 150 57 8550 -3.68 13..5424 2031.36 175 62 10850 +1.32 1.7424 304.92 75 67 5025 +6.32 39.9424 2995.68 15 72 1080 +11.32 128.1424 1922.14 10 77 770 +16.32 266.3424 2663.42 475 28,825 14,802.64 a. 28,825 60.68 475 x = = b. 2 14,802.64 31.23 474 s = = 31.23 5.59 s = = 71. f i M i f i M i M x i ( ) M x i 2 f M x i i ( ) 2 2 29.5 59.0 -22 484 968 6 39.5 237.0 -12 144 864 4 49.5 198.0 -2 4 16 4 59.5 238.0 8 64 256 2 69.5 139.0 18 324 648 2 79.5 159.0 28 784 1568 20 1,030.0 4320 1030 51.5 20 x = = 4320 227.37 19 s = = s = 15.08
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  • Spring '08
  • Staff
  • Standard Deviation, Descriptive statistics, standard deviations, x=, Σxi

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