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# Ch 14 Answers - Chapter 14 Chi-Square Tests 14.1 a b c d e...

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Chapter 14 Chi-Square Tests 14.1 a. H 0 : Earnings and Approach are independent. b. Degrees of Freedom = ( r - 1)( c - 1) = (4 - 1)(3 - 1) = 6 c. CHIINV(.01,6) = 16.81 and test statistic = 127.57. d. Test statistic is 127.57 ( p < .0001) so reject the null at α = .01. e. No Clear Effect and Business Combinations contributes the most. f. All expected frequencies exceed 5. g. p -value is near zero (observed difference not due to chance). Increase Decrease No Effect Total Expenses and Losses Observed 133 113 23 269 Expected 142.07 83.05 43.88 269.00 (O - E)² / E 0.58 10.80 9.93 21.31 Revenue and Gains Observed 86 20 8 114 Expected 60.21 35.20 18.59 114.00 (O - E)² / E 11.05 6.56 6.04 23.64 Business Combinations Observed 12 22 33 67 Expected 35.39 20.69 10.93 67.00 (O - E)² / E 15.46 0.08 44.58 60.12 Other Approaches Observed 41 4 20 65 Expected 34.33 20.07 10.60 65.00 (O - E)² / E 1.30 12.87 8.33 22.49 Total Observed 272 159 84 515 Expected 272.00 159.00 84.00 515.00 (O - E)² / E 28.38 30.31 68.88 127.57 127.57 chi-square 6 df p-value 14.2 a. H 0 : Age Group and Ownership are independent. b. Degrees of Freedom = ( r - 1)( c - 1) = (2 - 1)(4 - 1) = 3 c. CHIINV(.01,3) = 11.34 and test statistic = 19.31. d. Since the p -value (.0002) is less than .01, we reject the null and find dependence. e. Adults and Europe and Adults and Latin America contribute the most. f. All expected frequencies exceed 5. g. The p -value from MegaStat shows that observed difference would arise by chance only 2 times in 10,000 samples if the two variables really were independent. 143

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U.S. Europe Asia Latin. America Total Observed 80 89 69 65 303 Expected 75.75 75.75 75.75 75.75 303.00 (O - E)² / E 0.24 2.32 0.60 1.53 4.68 Observed 20 11 31 35 97 Expected 24.25 24.25 24.25 24.25 97.00 (O - E)² / E 0.74 7.24 1.88 4.77 14.63 Observed 100 100 100 100 400 Expected 100.00 100.00 100.00 100.00 400.00 (O - E)² / E 0.98 9.56 2.48 6.29 19.31 19.31 chi-square 3 df .0002 p-value 14.3 a. H 0 : Verbal and Quantitative are independent b. Degrees of Freedom = ( r - 1) ( c - 1) = (3 - 1)(3 - 1) = 4 c. CHIINV(.005,4) = 14.86 and test statistic = 55.88. d. Test statistic is 55.88 ( p < .0001) so we reject the null at α = .005. e. The upper left cell ( Under 25 and Under 25 ) contributes the most. f. Expected frequency is less than 5 in two cells. g. p -value is nearly zero (observed difference not due to chance). Under 25 25 to 35 35 or More Total Under 25 Observed 25 9 1 35 Expected 10.50 14.00 10.50 35.00 (O - E)² / E 20.02 1.79 8.60 30.40 25 to 35 Observed 4 28 18 50 Expected 15.00 20.00 15.00 50.00 (O - E)² / E 8.07 3.20 0.60 11.87 35 or More Observed 1 3 11 15 Expected 4.50 6.00 4.50 15.00 (O - E)² / E 2.72 1.50 9.39 13.61 Total Observed 30 40 30 100 Expected 30.00 40.00 30.00 100.00 (O - E)² / E 30.81 6.49 18.58 55.88 55.88 chi-square 4 df .0000 p-value 14.4 a. H 0 : Privilege Level and Disciplinary Action are independent. b.
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Ch 14 Answers - Chapter 14 Chi-Square Tests 14.1 a b c d e...

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