Appendix Tables 787 788 Appendix Tables Table A.1 Cumulative Binomial Probabilities Appendix Tables 789 Table A.1 Cumulative Binomial Probabilities (cont.) 790 Appendix Tables Table A.1 Cumulative Binomial Probabilities (cont.) Table A.2 Cumulative Poisson Probabilities Appendix Tables 791 Table A.2 Cumulative Poisson Probabilities (cont.) 792 Appendix Tables Table A.3 Standard Normal Curve Areas Appendix Tables 793 Table A.3 Standard Normal Curve Areas (cont.) 794 Appendix Tables Table A.4 The Incomplete Gamma Function Appendix Tables 795 Table A.5 Critical Values for t Distributions 796 Appendix Tables Table A.6 Critical Values for Chi-Squared Distributions Appendix Tables 797 Table A.7 t Curve Tail Areas 798 Appendix Tables Table A.7 t Curve Tail Areas (cont.) Appendix Tables 799 Table A.8 Critical Values for F Distributions 800 Appendix Tables Table A.8 Critical Values for F Distributions (cont.) Appendix Tables 801 Table A.8 Critical Values for F Distributions (cont.) 802 Appendix Tables Table A.8 Critical Values for F Distributions (cont.) Appendix Tables 803 Table A.8 Critical Values for F Distributions (cont.) 804 Appendix Tables Table A.8 Critical Values for F Distributions (cont.) Appendix Tables 805 Table A.9 Critical Values for Studentized Range Distributions 806 Appendix Tables Table A.10 Chi-Squared Curve Tail Areas Appendix Tables 807 Table A.10 Chi-Squared Curve Tail Areas (cont.) 808 Appendix Tables Table A.11 Critical Values for the Ryan–Joiner Test of Normality Appendix Tables 809 Table A.12 Critical Values for the Wilcoxon Signed-Rank Test 810 Appendix Tables Table A.13 Critical Values for the Wilcoxon Rank-Sum Test Appendix Tables 811 Table A.14 Critical Values for the Wilcoxon Signed-Rank Interval 812 Appendix Tables Table A.15 Critical Values for the Wilcoxon Rank-Sum Interval Appendix Tables Table A.16 b Curves for t Tests 813 Answers to Odd-Numbered Exercises Chapter 1 This display brings out the gap in the data: 1. a. Houston Chronicle, Des Moines Register, Chicago There are no scores in the high 70’s. Tribune, Washington Post b. Capital One, Campbell Soup, Merrill Lynch, 13. a. 2 23 Stem units: 1.0 Prudential 3 2344567789 Leaf units: .10 c. Bill Jasper, Kay Reinke, Helen Ford, David Menendez 4 01356889 d. 1.78, 2.44, 3.50, 3.04 5 00001114455666789 6 0000122223344456667789999 3. a. In a sample of 100 DVD players, what are the chances that more than 20 need service while under warranty? 7 00012233455555668 What are the chances that none need service while still 8 02233448 under warranty? 9 012233335666788 b. What proportion of all DVD players of this brand and 10 2344455688 model will need service within the warranty period? 11 2335999 12 37 5. a. No, the relevant conceptual population is all scores of all students who participate in the SI in conjunction 13 8 with this particular statistics course. 14 36 b. The advantage of randomly allocating students to the 15 0035 two groups is that the two groups should then be fairly 16 comparable before the study. If the two groups perform 17 differently in the class, we might attribute this to the 18 9 treatments (SI and control). If it were left to students to choose, stronger or more dedicated students might b. A representative value could be the median, 7.0. gravitate toward SI, confounding the results. c. The data appear to be highly concentrated, except for c. If all students were put in the treatment group there a few values on the positive side. would be no results with which to compare the d. No, there is skewness to the right, or positive treatments. skewness. e. The value 18.9 appears to be an outlier, being more 7. One could generate a simple random sample of all single than two stem units from the previous value. family homes in the city, or a stratified random sample by taking a simple random sample from each of the ten 15. a. district neighborhoods. From each of the homes in the Relative sample the necessary data would be collected. This Number frequency would be an enumerative study because there exists a finite, identifiable population of objects from which to nonconforming Frequency (Freq/60) sample. 0 7 0.117 9. a. There could be several explanations for the variability 1 12 0.200 of the measurements. Among them could be measuring 2 13 0.217 error, (due to mechanical or technical changes across 3 14 0.233 measurements), recording error, differences in 4 6 0.100 weather conditions at time of measurements, etc. 5 3 0.050 This study involves a conceptual population. There is b. 6 3 0.050 no sampling frame. 7 1 0.017 11. 6 l 034 810.017 6 h 667899 1.001 7 l 00122244 Doesn’t add exactly to 1 because relative 7 h Stem ¼ tens frequencies have been rounded 8 l 001111122344 Leaf ¼ ones 8 h 5557899 9l 03 9h 58 814 Chapter 1 815 b. .917, .867, 1 À.867 ¼ .133 c. The center of the histogram is somewhere around b. Class Freq Rel freq Density 2 or 3 and it shows that there is some positive skewness in the data. 0– < 50 8 0.08 .0016 50– < 100 13 0.13 .0026 17. a. .375 100– < 150 11 0.11 .0022 .218 b. < c. .242 150– 200 21 0.21 .0042 < d. The histogram is very positively skewed. 200– 300 26 0.26 .0026 300– < 400 12 0.12 .0012 19. a. The number of subdivisions having no cul-de-sacs is 400– < 500 4 0.04 .0004 ¼ 17/47 .362, or 36.2%. The proportion having at 500– < 600 3 0.03 .0003 least one cul-de-sac is 30/47 ¼ .638, or 63.8%. 600– < 900 2 0.02 .00007 100 1.00 y: Count Percent 0 17 36.17 c. .79 1 22 46.81 2 6 12.77 23. Class Freq Class Freq 3 1 2.13 5 1 2.13 10– < 20 8 1.1– < 1.2 2 N ¼ 47 20– < 30 14 1.2– < 1.3 6 .362, .638 30– < 40 8 1.3– < 1.4 7 40– < 50 4 1.4– < 1.5 9 50– < 60 3 1.5– < 1.6 6 b. z: Count Percent 60– < 70 2 1.6– < 1.7 4 70– < 80 1 1.7– < 1.8 5 0 13 27.66 40 1.8– < 1.9 1 1 11 23.40 40 2 3 6.38 3 7 14.89 4 5 10.64 The original distribution is positively skewed. 5 3 6.38 The transformation creates a much more symmetric, 6 3 6.38 mound-shaped histogram. 8 2 4.26 N ¼ 47 25. a. Class interval Freq Rel. Freq. .894, .830 0–< 50 9 0.18 21. a. 50–< 100 19 0.38 Class Freq Rel freq 100–< 150 11 0.22 150–< 200 4 0.08 < 0– 100 21 0.21 200–< 250 2 0.04 < 100– 200 32 0.32 250–< 300 2 0.04 < 200– 300 26 0.26 300–< 350 1 0.02 < 300– 400 12 0.12 350–< 400 1 0.02 < 400– 500 4 0.04 > ¼ 400 1 0.02 < 500– 600 3 0.03 50 1.00 600– < 700 1 0.01 700– < 800 0 0.00 800– < 900 1 0.01 100 1.00 The distribution is skewed to the right, or positively skewed. There is a gap in the histogram, and what appears to be an outlier in the ‘500–550’ interval. The histogram is skewed right, with a majority of observations between 0 and 300 cycles. The class holding the most observations is between 100 and 200 cycles. 816 Chapter 1 decreased to any value at least 370 without changing b. Class interval Freq. Rel. Freq. the median. d. 6.18 min; 6.16 min 2.25 < 2.75 2 0.04 2.75 < 3.25 2 0.04 35. a. 125. 3.25 < 3.75 3 0.06 b. If 127.6 is reported as 130, then the median is 130, a substantial change. When there is rounding or grouping, 3.75 < 4.25 8 0.16 the median can be highly sensitive to a small change. 4.25 < 4.75 18 0.36 4.75 < 5.25 10 0.20 37. x~ ¼ 92; xtrð25Þ ¼ 95:07; xtrð10Þ ¼ 102:23; x ¼ 119:3 5.25 < 5.75 4 0.08 Positive skewness causes the mean to be larger than the 5.75 < 6.25 3 0.06 median. Trimming moves the mean closer to the median. 39. a. y ¼ x þ c, y~ ¼ x~ þ c The distribution of the natural logs of the original data b. y ¼ cx, y~ ¼ cx~ is much more symmetric than the original. 41. a. 25.8 b. 49.31 c. 7.02 d. 49.31 c. .56, .14. 43. a. 2887.6, 2888 b. 7060.3 29. d. The frequency distribution is: 45. 24.36 Relative Relative 47. $1,961,160 Class frequency Class frequency 49. À3.5; 1.3, 1.9, 2.0, 2.3, À2.5 0 < 150 .193 900 < 1050 .019 51. a. 1, 6, 5 150 < 300 .183 1050 < 1200 .029 b. The box plot shows positive skewness. The two 300 < 450 .251 1200 < 1350 .005 longest runs are extreme outliers. 450 < 600 .148 1350 < 1500 .004 c. outlier: greater than 13.5 or less than À6.5 À 600 < 750 .097 1500 < 1650 .001 extreme outlier: greater than 21 or less than 14 d.