Solution Manual for Business Statistics, 3rd Edition

CHAPTER 2 Displaying Descriptive Statistics 2.1 a) 27  128  100 therefore use 7 classes. b) 29  512  300 therefore use 9 classes. c) 210  1,024  1,000 therefore use 10 classes. d) 211  2,048  2,000 therefore use 11 classes. 2.2 26  64  50 therefore use 6 classes. 74  16 Estimated Class Width   9.7  10 6 a) 16-25, 26-35, 36-45, 46-55, 56-65, 66-75 b) 16 to under 26, 26 to under 36, 36 to under 46, 46 to under 56, 56 to under 66, 66 to under 76 2.3 Frequency Number 1 2 3 4 5 Total 6 6 5 4 3 24 Relative Frequency 0.250 0.250 0.208 0.167 0.125 1.00 Cumulative Relative Frequency 0.250 0.500 0.708 0.875 1.00 2.4 25  32  30 therefore use 5 classes. 42.8  13.9 Estimated Class Width   5.8  6 5 2-1 Copyright ©2020 Pearson Education, Inc. 2-2 Chapter 2 Frequency Class 13 to less than 19 19 to less than 25 25 to less than 31 31 to less than 37 37 to less than 43 Total 6 11 4 7 2 30 Relative Frequency 0.200 0.367 0.133 0.233 0.067 1.00 Cumulative Relative Frequency 0.200 0.567 0.700 0.933 1.0 2.5 26  64  36 therefore use 6 classes. $5,927  $162 Estimated Class Width   $960  $1, 000 6 a, b, c) Frequency Class Less than $1,000 $1,000 to less than $2,000 $2,000 to less than $3,000 $3,000 to less than $4,000 $4,000 to less than $5,000 $5,000 to less than $6,000 Total 12 8 3 2 6 5 36 Relative Frequency 0.333 0.222 0.083 0.056 0.167 0.139 1.000 Cumulative Relative Frequency 0.333 0.555 0.638 0.694 0.861 1.000 d) The following histogram was constructed using bins $999, $1,999, $2,999, $3,999, $4,999, and $5,999. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-3 2.6 25  32  25 therefore use 5 classes. 46  18 Estimated Class Width   5.6  6 5 a, b, c) Frequency Class 18-23 24-29 30-35 36-41 42-47 Total 2 6 5 5 7 25 Relative Frequency 0.08 0.24 0.20 0.20 0.28 1.00 Cumulative Relative Frequency 0.08 0.32 0.52 0.72 1.00 d) The following histogram was constructed using bins 23, 29, 35, 41, and 47. Copyright ©2020 Pearson Education, Inc. 2-4 Chapter 2 2.7 a, b, c) Frequency Number 0 1 2 3 4 Total 3 21 23 15 8 70 Relative Frequency 0.043 0.300 0.329 0.214 0.114 1.000 Cumulative Relative Frequency 0.043 0.343 0.672 0.886 1.000 d) The following histogram was constructed using bins 0, 1, 2, 3, and 4. 2.8 26  64  40 therefore use 6 classes. 76  19 Estimated Class Width (Current)   9.5  10 6 Results would be similar using the laid-off ages. Class 19 to less than 29 29 to less than 39 39 to less than 49 49 to less than 59 59 to less than 69 69 to less than 79 Bins 28.9 38.9 48.9 58.9 68.9 78.9 Midpoint 24 34 44 54 64 74 Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-5 An extra bin (18.9) was added to Excel to provide the open-ended class required by PHStat. a) b) According to these ogives, it appears that the current workforce is younger than the laid-off employees. It appears that the laid-off employees may have a case for age discrimination. 2.9 29  512  350 therefore use 9 classes. $349.99  $2.19 Estimated Class Width   $38.64  $40 9 a, b, c) Frequency Class Less than $40 $40 to less than $80 $80 to less than $120 $120 to less than $160 $160 to less than $200 $200 to less than $240 $240 to less than $280 $280 to less than $320 $320 to less than $360 Total 52 103 91 65 15 11 5 5 3 350 Relative Frequency 0.149 0.294 0.260 0.186 0.043 0.031 0.014 0.014 0.009 1.000 Cumulative Relative Frequency 0.149 0.443 0.703 0.889 0.932 0.963 0.977 0.991 1.000 Copyright ©2020 Pearson Education, Inc. 2-6 Chapter 2 d) The following histogram was constructed using bins 39.999, 79.999, 119.999, 159.999, 199.999, 239.999, 279.999, 319.999, and 359.999. 2.10 27  128  125 therefore use 7 classes. 83.2  71.0 Estimated Class Width   1.7  2 7 a, b, c) Frequency Class 71 to less than 73 73 to less than 75 75 to less than 77 77 to less than 79 79 to less than 81 81 to less than 83 83 to less than 85 Total 5 37 44 31 6 1 1 125 Relative Frequency 0.040 0.296 0.352 0.248 0.048 0.008 0.008 1.000 Cumulative Relative Frequency 0.040 0.336 0.688 0.936 0.984 0.992 1.000 d) The following histogram was constructed using bins 72.99, 74.99, 76.99, 78.99, 80.99, 82.99, and 84.99. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-7 e) For 68.8% of the days, ocean temps were lower than 77 degrees. 2.11 a, b, c) Frequency Category Google Yahoo Bing Baidu Other Total 20 5 2 2 1 30 Relative Frequency 0.667 0.167 0.067 0.067 0.033 1.000 Cumulative Relative Frequency 0.667 0.833 0.900 0.967 1.000 Copyright ©2020 Pearson Education, Inc. 2-8 Chapter 2 d) 2.12 a, b, c) Frequency Category Excellent Good Fair Poor Total 16 31 8 5 60 Relative Frequency 0.267 0.517 0.133 0.083 1.000 Cumulative Relative Frequency 0.267 0.783 0.917 1.000 d) e) 78.3% rated their dining experience as either Excellent or Good. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-9 2.13 2.14 Copyright ©2020 Pearson Education, Inc. 2-10 Chapter 2 2.15 2.16 Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-11 2.17 2.18 2.19 Because all the possible categories appear to be included in the data, a pie chart would be a good choice to display this data. Copyright ©2020 Pearson Education, Inc. 2-12 Chapter 2 2.20 Because we are comparing data from a sample of countries over different time periods, a clustered bar chart would be a good choice to display this data. A stacked bar chart would not be the best choice because adding the GDPs for 2 time periods that are 10 years apart is not very meaningful. 2.21 Grade A B C Total Female 5 5 2 12 Male 2 7 3 12 Total 7 12 5 24 71% (5/7) of the As were earned by females even though they comprise of 50% (12/24) of the students in the class. The females appear to have done better grade-wise than the males. 2.22 Rating 1 2 3 4 Total Darby 0 2 6 7 15 Exton 2 3 7 3 15 Media 3 8 7 2 20 Total 5 13 20 12 50 Darby received 58% (7/12) of the 4-star ratings even though they were only 30% (15/50) of the surveyed customers. Darby appears to have higher customer satisfaction when compared to the other two locations. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-13 2.23 7|12345889 8|036677 9|00479 10 | 0 1 7 7 11 | 0 1 1 2 5 6 8 12 | 0 0 2 5 6 13 | 0 4 4 7 9 2.24 10 | 0 2 5 8 8 9 11 | 0 1 2 3 3 4 4 5 12 | 1 1 1 2 3 3 5 6 7 7 9 13 | 0 2 2 6 7 7 7 9 14 | 0 0 2 5 6 15 | 0 2.25 a) 1|36 2|123479 3|57778 4|00123344557889 5|0011224589 6|47 b) 1 (0) | 3 1 (5) | 6 2 (0) | 1 2 3 4 2 (5) | 7 9 3 (0) | 3 (5) | 5 7 7 7 8 4 (0) | 0 0 1 2 3 3 4 4 4 (5) | 5 5 7 8 8 9 5 (0) | 0 0 1 1 2 2 4 5 (5) | 5 8 9 6 (0) | 4 6 (5) | 7 Copyright ©2020 Pearson Education, Inc. 2-14 Chapter 2 2.26 a) 1|788 2|0 1233444556667788889 3|01 b) 1 (5) | 7 8 8 2 (0) | 0 1 2 3 3 4 4 4 2 (5) | 5 5 6 6 6 7 7 8 8 8 8 9 3 (0) | 0 1 2.27 It appears that the number of Netflix subscribers is increasing during this time period. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-15 2.28 There does not appear to be a consistent relationship between the amount of time on the web site and the order size. 2.29 2.30 26  64  40 therefore use 6 classes. 23  0 Estimated Class Width   3.8  4 6 Copyright ©2020 Pearson Education, Inc. 2-16 Chapter 2 a, b, c) Frequency Class 0-3 4-7 8-11 12-15 16-19 20-23 Total 8 5 15 3 6 3 40 Relative Frequency 0.200 0.125 0.375 0.075 0.150 0.075 1.000 Cumulative Relative Frequency 0.200 0.325 0.700 0.775 0.925 1.000 d) The following histogram was constructed using bins 3, 7, 11, 15, 19, and 23. 2.31 a, b, c) Frequency Cumulative Relative Frequency 0.32 0.50 0.64 0.86 0.96 1.00 Relative Number Frequency 0 16 0.32 1 9 0.18 2 7 0.14 3 11 0.22 4 5 0.10 5 2 0.04 Total 50 1.00 d) The following histogram was constructed using bins 0, 1, 2, 3, 4, and 5. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-17 e) 50% 2.32 26  64  48 therefore use 6 classes. 1,187  43 Estimated Class Width   190.7  200 6 a, b, c) Frequency Class 0 to under 200 200 to under 400 400 to under 600 600 to under 800 800 to under 1,000 1,000 to under 1,200 Total 15 13 11 4 4 1 48 Relative Frequency 0.313 0.271 0.229 0.083 0.083 0.021 1.000 Cumulative Relative Frequency 0.313 0.584 0.813 0.896 0.979 1.000 d) The following histogram was constructed using bins 199.9, 399.9, 599.9, 799.9, 999.9, and 1,199.9. Copyright ©2020 Pearson Education, Inc. 2-18 Chapter 2 2.33 27  128  72 therefore use 7 classes. 795  190 Estimated Class Width   86.4  100 7 a, b, c) Frequency Class 101-200 201-300 301-400 401-500 501-600 601-700 701-800 Total 2 2 9 15 31 9 4 72 Relative Frequency 0.028 0.028 0.125 0.208 0.431 0.125 0.056 1.001 Cumulative Relative Frequency 0.028 0.056 0.181 0.389 0.820 0.945 1.001 d) The following histogram was constructed using bins 200, 300, 400, 500, 600, 700, and 800. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-19 2.34 25  32  30 therefore use 5 classes. 100  66 Estimated Class Width (Day)   6.8  7 5 Results would be similar using the evening grades. Class 66-72 73-79 80-86 87-93 94-100 Bins 72 79 86 93 100 Midpoint 69 76 83 90 97 An extra bin (65) was added to Excel to provide the open-ended class required by PHStat. Copyright ©2020 Pearson Education, Inc. 2-20 Chapter 2 a) b) The evening class grades appear to be noticeably higher than the day class grades. 2.35 29  512  300 therefore use 9 classes. 39   14  Estimated Class Width   5.9  6 9 a, b, c) Frequency Class –14 to under –8 –8 to under –2 –2 to under 4 4 to under 10 10 to under 16 16 to under 22 22 to under 28 28 to under 34 34 to under 40 Total 6 28 40 58 68 61 27 9 3 300 Relative Frequency 0.020 0.093 0.133 0.193 0.227 0.203 0.090 0.030 0.010 0.999 Relative Cumulative Frequency 0.020 0.113 0.246 0.439 0.666 0.869 0.959 0.989 0.999 Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-21 d) The following histogram was constructed using bins –8.1, –2.1, 3.9, 9.9, 15.9, 21.9, 27.9, 33.9, and 39.9. e) Approximately 226 out of 300 flights were not late (75.3%). 2.36 a) Copyright ©2020 Pearson Education, Inc. 2-22 Chapter 2 b) 2.37 27  128  100 therefore use 7 classes. 259  12 Estimated Class Width (Wayne)   35.3  40 7 Results would be similar using the Dover data. Class 1-40 41-80 81-120 121-160 161-200 201-240 241-280 Bins 40 80 120 160 200 240 280 Midpoint 20.5 60.5 100.5 140.5 180.5 220.5 260.5 An extra bin (0) was added to Excel to provide the open-ended class required by PHStat. a) Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-23 b) It appears that the days on the market for homes sold in Wayne are longer than for homes sold in Dover. 2.38 a) Copyright ©2020 Pearson Education, Inc. 2-24 Chapter 2 b) 2.39 2.40 Reason Too long on hold Not knowledgeable Not courteous Hard to understand Too many transfers Other Total Frequency 47 22 18 15 10 8 120 Relative Frequency 0.392 0.183 0.150 0.125 0.083 0.067 Cumulative Relative Frequency 0.392 0.575 0.725 0.850 0.933 1.000 Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-25 2.41 Complaint Seat belts / air bags problems Engine problems Fuel System problems Body / paint problems Electrical problems Brakes problems Drivetrain problems Transmission problems Interior accessories problems Lights problems Suspension problems Miscellaneous problems Windows / windshield problems Wheels / hubs problems Cooling system problems Exterior accessories problems Clutch problems Steering problems Exhaust system problems Cumulative Relative Relative Frequency Frequency Frequency 182 0.428 0.428 54 0.127 0.555 40 0.094 0.649 28 0.066 0.715 25 0.059 0.774 23 0.054 0.828 15 0.035 0.864 9 0.021 0.885 7 0.016 0.901 7 0.016 0.918 7 0.016 0.934 6 0.014 0.948 5 5 4 3 3 1 1 0.012 0.012 0.009 0.007 0.007 0.002 0.002 0.960 0.972 0.981 0.988 0.995 0.998 1.000 425 Copyright ©2020 Pearson Education, Inc. 2-26 Chapter 2 2.42 Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-27 2.43 2.44 2.45 A bar chart would be appropriate for categorical data. The time data needs to be converted to common units (minutes). Copyright ©2020 Pearson Education, Inc. 2-28 Chapter 2 2.46 A clustered bar chart would be appropriate for this data. A stacked bar chart would also be an option. 2.47 A pie chart is the best choice for this data. The pie chart best illustrates the dominant position of Android. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-29 2.48 A pie chart is the best choice because all categories are included and the percentage sums to 100%. 2.49 A bar chart, either horizontal or vertical, is the best choice for this data. Copyright ©2020 Pearson Education, Inc. 2-30 Chapter 2 2.50 A bar chart is the best display for qualitative data organized in categories. 2.51 A bar chart is the best display for quantitative data organized in categories. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-31 2.52 Pie charts are a good choice for displaying qualitative data when the proportions add to 100%. 2.53 A stacked bar chart is the best choice to compare totals from different groups. 2.54 26  64  55 therefore use 6 classes. 66  26 Estimated Class Width   6.7  7 6 Copyright ©2020 Pearson Education, Inc. 2-32 Chapter 2 a, b, c) Frequency Class 26-32 33-39 40-46 47-53 54-60 61-67 Total 11 10 16 12 4 2 55 Relative Frequency 0.200 0.182 0.291 0.218 0.073 0.036 1.00 Cumulative Relative Frequency 0.200 0.382 0.673 0.891 0.964 1.00 d) The following histogram was constructed using bins 32, 39, 46, 53, 60 and 67. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-33 2.55 A pie chart is the best choice because the probabilities add to 100%. 2.56 a, b, c) Frequency Class 0 1 2 3 4 5 6 7 Total 2 1 13 16 11 10 4 3 60 Relative Frequency 0.033 0.017 0.217 0.267 0.183 0.167 0.067 0.050 1.001 Cumulative Relative Frequency 0.033 0.050 0.267 0.554 0.717 0.884 0.951 1.001 Copyright ©2020 Pearson Education, Inc. 2-34 Chapter 2 d) The following histogram was constructed using bins 0, 1, 2, 3, 4, 5, 6 and 7. 2.57 a) 6|47799 7|000111456778 8|123567789 9|0015678 10 | 2 4 11 | 7 b) 6 (0) | 4 6 (5) | 7 7 9 9 7 (0) | 0 0 0 1 1 1 4 7 (5) | 5 6 7 7 8 8 (0) | 1 2 3 8 (5) | 5 6 7 7 8 9 9 (0) | 0 0 1 9 (5) | 5 6 7 8 10 (0) | 2 4 10 (5) | 11 (0) | 11 (5) | 7 Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-35 2.58 As the number of household members increase, the average monthly food costs also tend to increase. 2.59 Copyright ©2020 Pearson Education, Inc. 2-36 Chapter 2 2.60 2.61 a, b, c) Frequency Category Cheez-Its Cheese Nips No Prefer Total 16 5 3 24 Relative Frequency 0.667 0.208 0.125 1.000 Cumulative Relative Frequency 0.667 0.875 1.000 2.62 1|2358 2|11366778 3|0335669 4|00224679 5|017 Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-37 2.63 2.64 Brand Coke Mt. Dew Pepsi Total Diet 6 2 4 12 Regular 6 8 7 21 Total 12 10 11 33 50% (6/12) of the Coke customers preferred Diet even though only 36% (12/33) of all the customers prefer Diet soda. Coke customers appear to have a higher percentage of customers who prefer diet soda than other brands. 2.65 Age 20-29 30-39 40-49 50-59 Total Callaway 4 9 16 3 32 Nike 2 15 6 3 26 Taylor Made 19 10 8 5 42 Total 25 34 30 11 100 Younger golfers seem to prefer Taylor Made clubs while older golfers seem to refer Callaway. Copyright ©2020 Pearson Education, Inc. 2-38 Chapter 2 2.66 a) 1|899 2|0002233555688889 3|011112235556699 4|13356 5|1 b) 1 (5) | 8 9 9 2 (0) | 0 0 0 2 2 3 3 2 (5) | 5 5 5 6 8 8 8 8 9 3 (0) | 0 1 1 1 1 2 2 3 3 (5) | 5 5 5 6 6 9 9 4 (0) | 1 3 3 4 (5) | 5 6 5 (0) | 1 2.67 a) 7|0022456777 8|1258 9|0122333457799 10 | 0 1 2 4 5 11 | 2 8 9 12 | 5 13 | 0 0 1 8 b) 7 (0) | 0 0 2 2 4 7 (5) | 5 6 7 7 7 8 (0) | 1 2 8 (5) | 5 8 9 (0) | 0 1 2 2 3 3 3 4 9 (5) | 5 7 7 9 9 10 (0) | 0 1 2 4 10 (5) | 5 11 (0) | 2 11 (5) | 8 9 12 (0) | 12 (5) | 5 13 (0) | 0 0 1 13 (5) | 8 Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-39 2.68 There does appear no more than a very weak, positive relationship between payroll and wins during the 2017 season. 2.69 Copyright ©2020 Pearson Education, Inc. 2-40 Chapter 2 The trend in gasoline prices was a consistent rise until the crisis in 2008. After that crisis, gasoline prices returned to the high levels of around $3.5 during 2011 to 2014. In 2014 and 2105, prices fell down to $2.00, with a modest rise afterwards. 2.70 a) Status Airline Delta Southwest United Total Late 5 5 7 17 On Time 38 22 23 83 Total 43 27 30 100 On Time 0.38 0.22 0.23 0.83 Total 0.43 0.27 0.30 1.00 b) Status Airline Delta Southwest United Total Late 0.05 0.05 0.07 0.17 c) Delta has the highest on-time percentage (38/43 = 0.88) while United has the lowest (23/30 = 0.77) 2.71 Using Chicago data, 26  64  60 therefore use 6 classes. 85  1 Estimated Class Width   14.0  15 6 Class 0 to less than 15 15 to less than 30 30 to less than 45 45 to less than 60 60 to less than 75 75 to less than 90 Bins 14.9 29.9 44.9 59.9 74.9 89.9 Midpoint 7.5 22.5 37.5 52.5 67.5 82.5 An extra bin (–0.1) was added to Excel to provide the open-ended class required by PHStat. Copyright ©2020 Pearson Education, Inc. Displaying Descriptive Statistics 2-41 Copyright ©2020 Pearson Education, Inc. 2-42 Chapter 2 2.72 A line chart would be the best display for these data. Note: the data set runs from 1959 to 2017, not 1970 to 2017 Copyright ©2020 Pearson Education, Inc.