Chapter 03 25. A normal population has 99.73 percent of the population measurements within __________ standard deviation(s) of the mean. A. 1 B. 2 C. 3 D. 4 AACSB: Reflective Thinking Blooms: Remember Difficulty: 2 Medium Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 26. All of the following are measures of central tendency except the ____________. A. range B. mode C. mean D. median AACSB: Reflective Thinking Blooms: Remember Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 27. Which percentile describes the first quartile, Q1? A. B. C. D. 25th 50th 75th 100th AACSB: Reflective Thinking Blooms: Remember Difficulty: 1 Easy Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 28. A. B. C. D. Which percentile describes the third quartile, Q3? 25th 50th 75th 100th AACSB: Reflective Thinking Blooms: Remember Difficulty: 1 Easy Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 29. Which of the following is influenced the least by the occurrence of extreme values in a sample? A. mean B. median C. geometric mean 3-1 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. D. weighted mean AACSB: Reflective Thinking Blooms: Understand Difficulty: 2 Medium Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 30. If a population distribution is skewed to the right, then, given a random sample from that population, one would expect that the ____________. A. B. C. D. median would be greater than the mean mode would be equal to the mean median would be less than the mean median would be equal to the mean AACSB: Reflective Thinking Blooms: Evaluate Difficulty: 3 Hard Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 31. If the mean, median, and mode for a given population all equal 25, then we know that the shape of the distribution of the population is ____________. A. B. C. D. bimodal skewed to the right symmetrical skewed to the left AACSB: Reflective Thinking Blooms: Understand Difficulty: 3 Hard Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 32. A disadvantage of using grouping (a frequency table) with sample data is that A. calculations involving central tendency and variation are more complicated than central tendency and variation calculations based on ungrouped data. B. the descriptive statistics are less precise than the descriptive statistics obtained using ungrouped data. C. the interpretation of the grouped data descriptive statistics is meaningless. D. it is much more difficult to summarize the information than it is with the ungrouped data. AACSB: Reflective Thinking Blooms: Evaluate Difficulty: 3 Hard Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 33. When using Chebyshev'sTheorem to obtain the bounds for 99.73 percent of the values in a population, the interval generally will be ___________ the interval obtained for the same percentage if a normal distribution is assumed (Empirical Rule). A. shorter than 3-2 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. B. wider than C. the same as AACSB: Reflective Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 34. A quantity that measures the variation of a population or a sample relative to its mean is called the ____________. A. B. C. D. E. range standard deviation coefficient of variation variance interquartile range AACSB: Reflective Thinking Blooms: Remember Difficulty: 1 Easy Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 35. As a measure of variation, the sample ___________ is easy to understand and compute. It is based on the two extreme values and is therefore a highly unstable measure. A. B. C. D. E. range standard deviation variance interquartile range coefficient of variation AACSB: Reflective Thinking Blooms: Understand Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 36. A measurement located outside the upper limits of a box-and-whiskers display is ___________. A. always in the first quartile B. an outlier C. always the largest value in the data set 3-3 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. D. within the lower limits AACSB: Reflective Thinking Blooms: Understand Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 37. Another name for the 50th percentile is the ___________. A. B. C. D. E. mean first quartile median mode third quartile AACSB: Reflective Thinking Blooms: Remember Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 38. The measurement in a sample or a population that occurs most frequently is the ___________. A. B. C. D. E. mode mean median outlier average AACSB: Reflective Thinking Blooms: Remember Difficulty: 2 Medium Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 39. The average of the squared deviations of the individual population measurement from the population mean is the ___________. A. B. C. D. E. standard deviation mean variance median range AACSB: Reflective Thinking Blooms: Remember Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 40. If the mean is greater than the median, then the distribution is ___________. A. skewed right 3-4 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. B. skewed left C. symmetrical D. bimodal AACSB: Reflective Thinking Blooms: Understand Difficulty: 2 Medium Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 41. The point estimate of the _______________ is the positive square root of the sample variance. A. B. C. D. E. sample mean sample standard deviation range median population standard deviation AACSB: Reflective Thinking Blooms: Understand Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 42. The ______________ is a quantity that measures the variation of a population or sample relative to its mean. A. B. C. D. E. mean standard deviation range coefficient of variation Z-score AACSB: Reflective Thinking Blooms: Understand Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 43. An interval that contains a specified percentage of the individual measurements is called a(n) _______________ interval. A. B. C. D. three-sigma tolerance normal empirical AACSB: Reflective Thinking Blooms: Understand Difficulty: 2 Medium Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 44. As the coefficient of variation _______________, risk ______________. A. increases, decreases 3-5 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. B. decreases, increases C. increases, increases D. remains constant, increases AACSB: Reflective Thinking Blooms: Evaluate Difficulty: 2 Medium Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 45. Which of the following is a measure of the strength of the linear relationship between x and y that is dependent on the units in which x and y are measured. A. B. C. D. covariance correlation coefficient slope least squares line AACSB: Reflective Thinking Blooms: Understand Difficulty: 2 Medium Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 46. If b0 = 32 and b1 = −4 and the predicted value of y is 14, what is the value of x? A. B. C. D. −24.0 18.0 4.5 0.56 AACSB: Reflective Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 47. In the least squares line, ___________ is defined as rise/run. A. B. C. D. correlation coefficient predicted value of y y-intercept slope AACSB: Reflective Thinking Blooms: Remember Difficulty: 1 Easy Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 48. In the calculation of a mean for grouped data, ___________ are used. A. total sample size and sum of the midpoints of each class B. total sample size and sum of the weighted midpoints C. sum of the frequency of each class and the sum of the midpoints of each class 3-6 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. D. sum of the frequency of each class and the sample midpoint AACSB: Reflective Thinking Blooms: Understand Difficulty: 3 Hard Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 49. The arithmetic mean is ___________ larger than a weighted mean in a set of data that uses unequal weights. A. always B. sometimes C. never AACSB: Reflective Thinking Blooms: Understand Difficulty: 3 Hard Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 50. The constant return used to forecast future wealth based on actual time periods and their returns is the ____________. A. B. C. D. grouped mean geometric mean weighted mean arithmetic mean AACSB: Reflective Thinking Blooms: Remember Difficulty: 1 Easy Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Geometric Mean 51. In a statistics class, the following 10 scores were randomly selected: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the mean? A. B. C. D. E. 71.5 72.0 77.0 71.0 73.0 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 52. In a statistics class, the following 10 scores were randomly selected: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the median? A. 71.5 B. 72.0 3-7 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. C. 77.0 D. 71.0 E. 73.0 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 53. In a statistics class, the following 10 scores were randomly selected: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the mode? A. B. C. D. E. 71.5 72.0 77.0 71.0 73.0 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 54. In a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are: 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68. What is the mean? A. B. C. D. E. 70 75 68 71 80 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 55. In a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are: 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68. What is the median? 3-8 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. A. B. C. D. E. 70 75 68 71 80 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 56. In a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are: 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68. What is the mode? A. B. C. D. E. 70 75 68 71 80 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 57. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118. What is the mean? A. 114.15 B. 118 C. 148 D. 45 E. 115.5 Mean = sum of values/n = 1484/13 = 114.15 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 58. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118. What is the median? A. 114.15 B. 118 3-9 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. C. 148 D. 45 E. 115.5 To calculate median, put data measurements in ascending order. The median for an odd number of measurements is the middle measurement;median = 118. AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 59. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118. What is the mode? A. 114.15 B. 118 C. 148 D. 45 E. 115.5 Mode is the value(s) that appears most frequently; mode = 118 (occurs three times). AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 60. Quality control is an important issue at ACME Company, which manufactures light bulbs. To test the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted: 378, 361, 350, 375, 200, 391, 375, 368, 321. What is the mean? A. B. C. D. E. 375 368 389.9 200 346.6 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 61. Quality control is an important issue at ACME Company, which manufactures light bulbs. To test the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted: 378, 361, 350, 375, 200, 391, 375, 368, 321. What is the median? A. 375 B. 368 3-10 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. C. 389.9 D. 200 E. 346.6 To calculate median, put data measurements in ascending order. The median for an odd number of measurements is the middle measurement;median = 368. AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 62. Quality control is an important issue at ACME Company, which manufactures light bulbs. Totest the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted: 378, 361, 350, 375, 200, 391, 375, 368, 321. What is the mode? A. 375 B. 368 C. 389.9 D. 200 E. 346.6 Mode is the value(s) that appear most frequently; mode = 375 (occurs two times). AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-01 Compute and interpret the mean, median, and mode. Topic: Describing Central Tendency 63. Find the coefficient of variation for IQ tests with a mean of 100 and a standard deviation of 15. A. 15.0 B. 6.7 C. 0.15 D. 1.5 E. 67 Coefficient of variation = (Stddev/mean) × 100 = (15/100) × 100 = 15 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 64. Find the z-score for an IQ test score of 142 when the mean is 100 and the standard deviation is 15. A. 42 B. 2.8 C. 18.78 D. 1.27 E. −2.8 3-11 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Z-score = (x − mean)/stddev = (142 − 100)/15 = 42/15 = 2.8 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 65. Find the z-score for an IQ test score of 92 when the mean is 100 and the standard deviation is 15. A. 0.53 B. 0.77 C. −0.77 D. −0.53 E. −8.00 Z-score = (x − mean)/stddev = (92 − 100)/15 = −8/15 = −0.53 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 66. Find the z-score for an IQ test score of 118 when the mean is 100 and the standard deviation is 15. A. 1.2 B. 1.0 C. 18.0 D. −1.03 E. −1.2 Z-score = (x − mean)/stddev = (118 − 100)/15 = 18/15 = 1.2 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 67. Find the z-score for an IQ test score of 125 when the mean is 100 and the standard deviation is 15. A. 25 B. 1.1 C. 1.67 D. −1.1 3-12 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. E. −1.67 Z-score = (x − mean)/stddev = (125 − 100)/15 = 25/15 = 1.67 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 68. Using Chebyshev'sTheorem, find the interval that contains at least 93.75 percentof all measurements when the mean = 2.549 and s = 1.828. A. [−2.935, 8.033] B. [−1.107, 6.205] C. [−26.699, 31.797] D. [2.435, 2.663] E. [−4.763, 9.861] 1 − (1/k2) = .9375; 1/k2 = 1 − .9375; 1/k = √.0625; k = 4 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 69. According to a survey of the top 10 employers in a major city in the Midwest, a worker spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8 minutes, and the time spent is approximately a normal distribution. What are the times within which approximately 68.26 percent of all workers will fall? A. B. C. D. E. [394.8, 431.2] [386.2, 439.8] [372.8, 453.2] [359.4, 466.6] [332.6, 493.4] AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 70. According to a survey of the top 10 employers in a major city in the Midwest, a worker spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8 minutes and the time spent is approximately a normal distribution. What are the times within which approximately 99.73 percent of all workers will fall? A. [305.8, 520.2] 3-13 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. B. C. D. E. [386.2, 439.8] [372.8, 453.2] [359.4, 466.6] [332.6, 493.4] AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 71. According to Chebyshev's Theorem, at least what proportion of the data will be within μ ± kσ for k = 2? A. B. C. D. E. 68% 50% 25% 75% 34% AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 72. According to Chebyshev's Theorem, at least what proportion of the data will be within μ ± kσ for k = 1.6? A. B. C. D. E. 39% 58% 68% 61% 92% AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 73. Using Chebyshev's Theorem, approximate the minimum proportion of the data that will be within μ ± kσ for k = 3.2. A. B. C. D. E. 90% 95% 84% 97% 10% AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 74. According to Chebyshev'sTheorem, a range of how many standard deviations would include at least 80 percentof the values? A. 5.0 B. 2.2 C. 2.5 D. 1.6 E. 2.0 AACSB: Analytical Thinking Blooms: Apply 3-14 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Difficulty: 3 Hard Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 75. In a statistics class, 10 scores were randomly selected with the following results (mean = 71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the range? A. B. C. D. E. 22.72 12.00 4.77 516.20 144.00 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 76. In a statistics class, 10 scores were randomly selected with the following results (mean = 71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the variance? A. B. C. D. E. 22.72 12.00 4.77 516.20 144.00 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 77. In a statistics class, 10 scores were randomly selected with the following results (mean = 71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the standard deviation? A. B. C. D. E. 22.72 12.00 4.77 516.20 144.00 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 78. In a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are (mean = 70): 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68. What is the range? 3-15 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. A. B. C. D. E. 18 4.73 22.40 324 6.76 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 79. In a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are (mean = 70): 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68. What is the variance? A. B. C. D. E. 18 4.73 22.40 324 6.76 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 80. In a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are (mean = 70): 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68. What is the standard deviation? A. B. C. D. E. 18 4.73 22.40 324 6.76 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 81. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes;mean = 114.15): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118. What is the range? 3-16 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. A. B. C. D. E. 103 23.62 557.97 128.8 115 Range = largest value − smallest value = 148 − 45 = 103 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 82. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes;mean = 114.15): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118. What is the variance? A. 103 B. 23.62 C. 557.97 D. 128.8 E. 115 Variance = [Σ (x− mean)2]/(n − 1) =6695.69/12 = 557.97 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 83. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes;mean = 114.15): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118. What is the standard deviation? A. 103 B. 23.62 3-17 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. C. 557.97 D. 128.8 E. 115 Std Dev = √Variance = √[(Σ (x− mean)2)/(n − 1)] = √(6695.69/12)= √557.97 = 23.62 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 84. Quality control is an important issue at ACME Company, which manufactures light bulbs. To test the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted (mean = 346.6). 378, 361, 350, 375, 200, 391, 375, 368, 321 What is the range? A. 342.43 B. 3424.3 C. 58.5 D. 191 E. 10,609 Range = largest value − smallest value = 391 − 200 = 191 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 85. Quality control is an important issue at ACME Company, which manufactures light bulbs. To test the life hours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted (mean = 346.6). 378, 361, 350, 375, 200, 391, 375, 368, 321 What is the variance? A. 342.43 B. 3424.3 C. 58.5 D. 191 E. 10,609 Variance = [Σ (x− mean)2]/(n − 1) =27,394.24/8 = 3424.28 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 86. Quality control is an important issue at ACME Company, which manufactures light bulbs. To test the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted (mean = 346.6). 378, 361, 350, 375, 200, 391, 375, 368, 321 What is the standard deviation? A. 342.43 B. 3424.3 C. 58.5 D. 191 E. 10,609 3-18 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Std Dev = √Variance = √[(Σ (x− mean)2)/(n − 1)] = √(27,394.24/8) = √3424.28 = 58.5 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 87. In a statistics class, 10 scores were randomly selected, with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the 90th percentile? A. B. C. D. E. 77 73 74 67 65.9 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 88. In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the third quartile? A. B. C. D. E. 65.9 67.3 66.75 73.85 77.0 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 89. In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the first quartile? A. B. C. D. E. 65.9 67.3 67.0 73.85 77.0 3-19 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 90. In a statistics class, 10 scores were randomly selected, with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the 10th percentile? A. B. C. D. E. 65.5 67.3 66.75 73.85 77.0 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 91. In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the 65th percentile? A. B. C. D. E. 65.5 67.3 66.75 74.0 77.0 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 92. In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the IQR? A. B. C. D. E. 12.00 5.25 10 5.00 11.00 3-20 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 93. In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What are the lower and upper limits? A. B. C. D. E. 67, 77 57, 87 37, 107 52, 92 47, 97 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 94. The company financial officer was interested in the average cost of PCs that had been purchased in the past six months. She took a random sample of the price of 10 computers, with the following results. $3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000 What is the 90th percentile? A. B. C. D. E. $1,446.50 $3,449.00 $3,415.75 $4,000.00 $5,060.00 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 95. The company financial officer was interested in the average cost of PCs that had been purchased in the past six months. She took a random sample of the price of 10 computers, with the following results. $3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000 What is the third quartile? A. $1,446.50 B. $2,617.00 C. $3,415.75 3-21 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. D. $3,449.00 E. $4,212.00 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 96. The company financial officer was interested in the average cost of PCs that had been purchased in the past six months. She took a random sample of the price of 10 computers, with the following results. $3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000 What is the first quartile? A. $1,446.50 B. $2,995.00 C. $3,415.75 D. $3,587.00 E. $4,212.00 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 97. The company financial officer was interested in the average cost of PCs that had been purchased in the past six months. She took a random sample of the price of 10 computers, with the following results. $3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000 What is the 10th percentile? A. $1,304.50 B. $2,617.00 C. $3,415.75 D. $3,587.00 E. $4,212.00 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 98. The company financial officer was interested in the average cost of PCs that had been purchased in the past six months. She took a random sample of the price of 10 computers, with the following results. $3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000 What is the 65th percentile? A. $1,446.50 B. $2,617.00 C. $3,445.00 3-22 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. D. $3,587.00 E. $4,212.00 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 99. The company financial officer was interested in the average cost of PCs that had been purchased in the past six months. She took a random sample of the price of 10 computers, with the following results. $3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000 What is the IQR? A. B. C. D. E. 681 454 1362 255 6120 IQR = Q3− Q1 = 3449 − 2995 = 454 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 100. The company financial officer was interested in the average cost of PCs that had been purchased in the past six months. She took a random sample of the price of 10 computers, with the following results. $3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000 What are the lower and upper limits? A. B. C. D. E. 2541, 3903 2768, 3676 2087, 4357 2314, 4130 1633, 2087 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 101. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes). 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118 What is the 90th percentile? 3-23 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. A. B. C. D. E. 100.8 118 130 112 45 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 102. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes). 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118 What is the third quartile? A. B. C. D. E. 100.8 118 130 112 121 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 103. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes). 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118 What is the first quartile? A. B. C. D. E. 100.8 118 130 116 45 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 104. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes). 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118 What is the 10th percentile? A. 99 B. 120 C. 130 3-24 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. D. 112 E. 45 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 105. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes). 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118 What is the 65th percentile? A. B. C. D. E. 99 120 130 112 45 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 106. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes). 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118 What is the IQR? A. B. C. D. E. 103 5 28 30 7 IQR = Q3− Q1 = 121 − 116 = 5 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 107. The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes). 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118 What are the lower and upper limits? 3-25 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. A. 80.5, 154.00 B. 108.5, 128.5 C. 127.75, 138.25 D. 80.5, 154.00 E. 143.50, 154.00 F. 127.75, 138.25 G. 15.75, 31.50 H. 143.50, 154.00 I. 15.75, 31.50 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 108. Compute the population variance of these data: 16,18,23,21,17,16,24,23,9,17,11,16,22,10,15,14. A. B. C. D. E. 21.9 3.87 20.5 17.0 3.625 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 109. If the median of a data set is 760, the upper quartile is 950, and the lower quartile is 650, what is the interquartile range? A. 300 B. 190 C. 110 D. 150 E. 910 Interquartile range = 950 − 650 = 300 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 110. Compute the sample standard deviation of the data set 6,4,2,1,4,1. A. B. C. D. E. 1.83 2.00 1.41 3.33 4.00 3-26 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 111. The average lateness for one of the top airline companies is 10 minutes. The variance of the lateness measure is calculated as 9. An airplane arrived 13 minutes after the stated arrival time. Calculate the z-score for the lateness of this particular airplane. A. B. C. D. E. 0.33 0.58 1.33 0.44 1.00 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation. Topic: Measures of Variation 112. The average life of Canadian women is 73.75 years, and the standard deviation of the life expectancy of Canadian women is 6.5 years. Using Chebyshev's Theorem, determine the minimum percentage of women in Canada whose life expectancy is between 64 and 83.5 years. A. B. C. D. E. 93.17% 68.26% 55.56% 88.89% 33.33% AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 113. The average life of Canadian women is 73.75 years, and the standard deviation of the life expectancy of Canadian women is 6.5 years. Based on Chebyshev's Theorem, determine the upper and lower bounds on the average life expectancy of Canadian women such that at least 90 percent of the population is included. A. B. C. D. E. [12.09 135.41] [8.75 138.75] [53.20 94.30] [66.38 81.13] [67.25 80.25] AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe variation. Topic: Measures of Variation 114. The following table shows the Price-to-Earnings ratio for a stereo equipment manufacturing company between 1998 and 2002. 3-27 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Determine the percentage change in the P/E ratios from 1998 to 1999. A. B. C. D. E. 15.07% 17.74% 20.72% −17.74% −15.07% AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 115. The following table shows the Price-to-Earnings ratio for a stereo equipment manufacturing company between 1998 and 2002. Determine the percentage change in the P/E ratios from 1999 to 2000. A. B. C. D. E. 23.97% 31.53% 27.26% −31.53% −23.97% AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 116. The following table shows the Price-to-Earnings ratio for a stereo equipment manufacturing company between 1998 and 2002. The annual percentage growth rate of the P/E ratios is also 3-28 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. calculated and given below. Calculate the geometric mean growth rate increase or decrease over the period from 1998 to 2002. A. B. C. D. E. −.2592 −.1397 −.1816 .8616 .7417 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 117. Suppose that a company's annual sales were $1,200,000 in 1999. The annual growth rate of sales from 1999 to 2000 was 16 percent, from 2000 to 2001 it was −5 percent, and from 2001 to 2002 it was 22 percent. The geometric mean growth rate of sales over this three-year period is calculated as 10.37 percent. Use the geometric mean growth rate and determine the forecasted sales for 2004. A. B. C. D. E. 1,780,678 1,200,014 1,965,337 1,613,371 1,422,197 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 118. The following frequency table summarizes the ages of 60 shoppers at the local grocery store. 3-29 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. The sample mean for the above frequency table is calculated as 36.25. Calculate the approximate sample standard deviation for this data set. A. B. C. D. E. 181.08 184.15 26.83 13.46 13.57 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 119. Personnel managers usually want to know where a job applicant ranked in his or her graduating class. With a grade point average of 3.83, Michelle Robinson graduated above the 93rd percentile of her graduating class. What is the percentile rank of a student whose GPA was the median GPA. A. B. C. D. E. 25th 50th 75th 10th 93rd AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers displays. Topic: Percentiles, Quartiles, and Box-and-Whisker Displays 120. The Rivertown city council is attempting to choose one of four sites (A, B, C, or D) as the location for its new emergency facility. After the new emergency facility becomes available for service, 3-30 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. the current emergency facility will be shut down. The project manager has estimated the following response times in minutes from each of the proposed sites to the four areas that must be served by the emergency facility. The number of emergency runs from the current emergency facility to each of the four areas over the past year is as follows: Compute the weighted mean response time from the proposed locations and determine which proposed site should be selected for the new emergency facility. A. B. C. D. site A site B site C site D AACSB: Analytical Thinking Blooms: Analyze Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 3-31 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 121. Researchers wish to study fuel consumption rates based on speed. The data from the test car at 10 speeds are below. It can be shown that for these data: Calculate the sample covariance. A. B. C. D. E. −270.2 −30.02 −27.02 −74.58 −82.86 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 3-32 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 122. Researchers wish to study fuel consumption rates based on speed. The data from the test car at 10 speeds are below. It can be shown that for these data: Calculate b1. −0.1148 3-33 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 123. Researchers wish to study fuel consumption rates based on speed. The data from 10 cars are below. It can be shown that for these data: Calculate the sample correlation coefficient. A. B. C. D. E. 0.12 −0.12 −0.36 −0.34 0.34 r = sxy/(sx sy) = −30.02/88.17 = −0.34 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 3-34 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 124. In a study of the factors that affect success in economics, data were collected for 8 business students. Scores on a calculus placement test are given with economics final exam scores. The data are below: It can be shown that for these data: Calculate the sample covariance. A. B. C. D. E. 0.12 −0.12 −0.36 −0.34 0.34 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 3-35 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 125. In a study of the factors that affect success in economics, data were collected for 8 business students. Scores on a calculus placement test are given with economics final exam scores. The data are below. It can be shown that for these data: Calculate the sample correlation coefficient. A. B. C. D. E. 0.15 0.11 0.39 −0.39 −0.11 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 3-36 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 126. In a study of employee stock ownership plans, data were collected at seven companies on satisfaction with the plan and the amount of organization commitment. It can be shown that for these data: Calculate b1. A. B. C. D. E. 0.15 0.11 0.39 −0.39 −0.11 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 3-37 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 127. In a study of employee stock ownership plans, data were collected at seven companies on satisfaction with the plan and the amount of organization commitment. It can be shown that for these data Calculate b1. 0.851 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares line. Topic: Covariance, Correlation, and the Least Squares Line 3-38 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 128. In an analysis of the relationship between the average weekly temperature in a major city and the per person consumption of ice cream (pints), a least squares line is defined by the equation 5.72 + .004x. Predict the average amount of ice cream consumed when it is 50° outside. 5.92 pints y = 5.72 + .004(50) = 5.92 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Covariance, Correlation, and the Least Squares Line Topic: Weighted Means and Grouped Data 129. From the following table of values and corresponding sample sizes, calculate the weighted mean. 4.1 (3.1 × 9 + 5.1 × 7 + 4.2 × 10 + 2.5 × 2 + 4.8 × 6)/34 = 139.4/34 = 4.1 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 130. Using grouped data of 14 classes with a sample mean of 51 and a sample variance of 6.42, calculate the group sampled standard deviation. 2.53 √6.42 = 2.53 AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 3-39 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 131. A random sample of 60 students in the business statistics course answered a survey on the average number of hours they spent on statistics each week. Unfortunately, the original data were lost and all that remains is the frequency table below. From these data, calculate the estimated sample mean. 6.97 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 3-40 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 132. A random sample of 60 students in the business statistics course answered a survey on the average number of hours they spent on statistics each week. Unfortunately, the original data were lost and all that remains is the frequency table below. From these data, calculate the estimated sample standard deviation. 4.714 Sample variance = (1310.934)/(n − 1) = 1310.934/59 = 22.21922 Sample standard deviation = √22.21922 = 4.713727 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 3-41 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 133. A real estate appraiser is gathering housing sales data by street in the neighborhood in preparation for his next job. Listed below are the six streets and the average sales price and the houses sold in the last 12 months. Calculate the mean sales price for the neighborhood. $213,602 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 134. A company CEO asked the marketing research department to find the average age of consumers who bought the most profitable product made by the company. From survey data gathered two years ago, the researchers found the following table. Calculate the average age to give to the CEO. 3-42 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. AACSB: Analytical Thinking Blooms: Apply Difficulty: 1 Easy Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 135. Find the weighted mean per capita income for the following random sample of six cities in the Midwest. $31,432 AACSB: Analytical Thinking Blooms: Apply 3-43 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Difficulty: 2 Medium Learning Objective: 03-06 Compute and interpret weighted means and the mean standard deviation of grouped data. Topic: Weighted Means and Grouped Data 136. An initial investment of $10,000 is observed over 3 years with a geometric mean return at the end of year 3 of 0.512. Determine the value of the investment after 3 years. $34,566 $10,000 (1 + .512)3 = 10,000(3.4566) = 34,566 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 137. An initial investment of $10,000 has a value of $7,382 at the end of year 1. What is the rate of return for the first year? −26.18% R1 = ((7382 − 10,000)/10,000) = −2618/10,000 = −.2618 × 100 = −26.18% AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 138. An initial investment of $10,000 has a value of $7,382 at the end of year 1, a rate of return of 62.43 percent for year 2, and a geometric mean return at the end of year 3 of 0.512. Determine the rate of return for the third year. 188.3% for R3 Rg = .512 = (3√(R1 + 1)(R2 + 1)(R3 + 1)) − 1 1.512 = (3√(R1 + 1)(R2 + 1)(R3 + 1)) 1.512 = 3√(-.2618 + 1)(.6243 + 1)(R3 + 1) 3.457 = (1.199)(R3 + 1) 2.883 = R3 + 1 1.883 = R3 R3 = 1.883 × 100 = 188.3% AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 3-44 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 139. At the end of 2007, the IRA owned by Joe Smith had a value of $1.2 million. With a rate of return of −29.75 percent in 2008 and a rate of return of 2.98 percent in 2009, calculate the geometric mean rate of return for the two-year period. −.1495 Rg = √[(1 − .2975)(1 + .0298)] − 1 = −.1495 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 140. The geometric mean growth rate of sales for used cars in a geographic area from 2005 to 2009 was 16.42 percent. Annual sales in 2005 were $14.2 million. Find the ending value of sales after this four-year period. $26.09 million 14.2(1 + .1642)4 = 26.09 AACSB: Analytical Thinking Blooms: Apply Difficulty: 2 Medium Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 141. Suppose that annual sales for a company were $3.6 million at the beginning of a three-year period and at the end had increased to $6.1 million. Find the geometric growth rate of sales. .19 3.6(1 + Rg)3 = 6.1 (1 + Rg)3 = 1.69 (1 + Rg) = 1.1911 Rg = .1911 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 3-45 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 142. The rate of return for each of the past four years on a market fund are R1 = 2.4%, R2 = 1.0%, R3 = −3.2%, and R4 = 0.5%. Find the geometric mean rate of return. .0015 Rg = (4√(1.024)(1.01)(.968)(1.005)) − 1 = (4√1.0062) − 1 = 1.0015 − 1 = .0015 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-07 Compute and interpret the geometric mean. Topic: Geometric Mean 143. A local grocery market is studying whether to offer a loyalty program to its customers. In its final analyses the following groups are being used to categorize loyalty card customers: family income and number of children. Using the classification tree below, estimate the percentage of customers with an income of $50,000 with 2 children who would use a loyalty card 40% Tree moves from Yes with income > 35,000 to yes have 1 or more children. This yields a probability of .4 or a percentage of 40% of the customers who would use a loyalty card. AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-08 Interpret the information provided by a decision tree. Topic: Decision Trees: Classification Trees and Regression Trees 3-46 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 144. A manufacturer of Product X has developed a model for predicting monthly sales of their product based on the sales from the same month of the previous year and the forecasted average daily temperature for the month. Using the regression tree below based on a random sample of 30 observations, predict sales for a future where the previous year’s monthly sales were $15 million dollars and the forecasted average daily temperature for the month will be 45 degrees. $15.4 Million Monthly sales < 18.1; then monthly sales < 16.1, which yields mean of 15.4. AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-08 Interpret the information provided by a decision tree. Topic: Decision Trees: Classification Trees and Regression Trees 3-47 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 145. A manufacturer of Product X has developed a model for predicting monthly sales of their product based on the sales from the same month of the previous year and the forecasted average daily temperature for the month. Using the regression tree below based on a random sample of 30 observations predict sales for a future where the previous year’s monthly sales were $21.2 million dollars and the forecasted average daily temperature for the month will be 45 degrees. $18.3 Million Monthly Sales ≥ 18.1; then Temp < 50 which yields mean of 18.3 AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-08 Interpret the information provided by a decision tree. Topic: Decision Trees: Classification Trees and Regression Trees 3-48 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 146. Following a factor analysis of 15 personality characteristic ratings of politicians by a random sample of 40,000 registered voters, the following table of the first 7 factors and their corresponding eigenvalues and percentage of explained variation was produced. Which factors should an analyst choose when defining the characteristics of politicians? Factors 1 , 2, 3, and 4 Use factors that have an eigenvalue greater than 1 AACSB: Analytical Thinking AACSB: Reflective Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-10 Interpret the information provided by factor analysis. Topic: Factor Analysis 3-49 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 147. Interpret a lift ratio of .9259. 7.41 percent of total population less likely to follow recommendation than a random customer. A lift ratio is calculated by dividing confidence percentage by support percentage. The difference from 1 is the percentage of a customer base that is or is not following recommendation from association rules. AACSB: Reflective Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-11 Interpret the information provided by association roles. Topic: Association Rules 148. Interpret a lift ratio of 1.111. 11.1 percent of total population more likely to follow recommendation than a random customer. A lift ratio is calculated by dividing confidence percentage by support percentage. The difference from 1 is the percentage of a customer base that is or is not following recommendation from association rules. AACSB: Reflective Thinking Blooms: Apply Difficulty: 3 Hard Learning Objective: 03-11 Interpret the information provided by association roles. Topic: Association Rules 3-50 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.