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business
essentials of statistics

Essentials Of Statistics For Business And Economics 5th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams - Solutions

14. An experiment has four equally likely outcomes: E1, E2, E3, and E4.a. What is the probability that E2 occurs?b. What is the probability that any two of the outcomes occur (e.g., E1 or E3)?c. What is the probability that any three of the outcomes occur (e.g., E1 or E2 or E4)?
13. A company that manufactures toothpaste is studying five different package designs.Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were
12. The Powerball lottery is played twice each week in 28 states, the Virgin Islands, and the District of Columbia. To play Powerball a participant must purchase a ticket and then select five numbers from the digits 1 through 55 and a Powerball number from the digits 1 through 42. To determine the
11. The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the United States are using seat belts (Associated Press, August 25, 2003). Sample data consistent with the NHTSA survey are as follows.c. What is the probability of seat belt
10. Venture capital can provide a big boost in funds available to companies. According to Venture Economics (Investor’s Business Daily, April 28, 2000), of 2374 venture capital disbursements, 1434 were to companies in California, 390 were to companies in Massachusetts, 217 were to companies in
9. Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about
8. In the city of Milford, applications for zoning changes go through a two-step process: a review by the planning commission and a final decision by the city council. At step 1 the planning commission reviews the zoning change request and makes a positive or negative recommendation concerning the
7. A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E1) .10, P(E2) .15, P(E3) .40, and P(E4) .20. Are these probability assignments valid? Explain.
6. An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 occurred 13 times, and E3 occurred 17 times. Assign probabilities to the outcomes. What method did you use?
5. Suppose an experiment has five equally likely outcomes: E1, E2, E3, E4, E5. Assign probabilities to each outcome and show that the requirements in equations (4.3) and (4.4) are satisfied. What method did you use?
4. Consider the experiment of tossing a coin three times.a. Develop a tree diagram for the experiment.b. List the experimental outcomes.c. What is the probability for each experimental outcome?
3. How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.
2. How many ways can three items be selected from a group of six items? Use the letters A, B, C, D, E, and F to identify the items, and list each of the different combinations of three items.
1. An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?
70. Automobiles traveling on a road with a posted speed limit of 55 miles per hour are checked for speed by a state police radar system. Following is a frequency distribution of speeds.
69. The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided. Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds.
68. A forecasting technique referred to as moving averages uses the average or mean of the most recent n periods to forecast the next value for time series data. With a three-period moving average, the most recent three periods of data are used in the forecast computation. Consider a product with
67. The following data show the trailing 52-week primary share earnings and book values as reported by 10 companies (The Wall Street Journal, March 13, 2000).a. Develop a scatter diagram for the data with book value on the x-axis.b. What is the sample correlation coefficient, and what does it tell
66. Road & Track provided the following sample of the tire ratings and load-carrying capacity of automobiles tires.a. Develop a scatter diagram for the data with tire rating on the x-axis.b. What is the sample correlation coefficient, and what does it tell you about the relationship between tire
65. The following data show the media expenditures ($ millions) and shipments in millions of barrels (bbls.) for 10 major brands of beer.a. What is the sample covariance? Does it indicate a positive or negative relationship?b. What is the sample correlation coefficient?
64. The National Association of Realtors reported the median home price in the United States and the increase in median home price over a five-year period (The Wall Street Journal, January 16, 2006). Use the sample home prices shown here to answer the following questions.995.9 48.8 175.0 263.5
63. Public transportation and the automobile are two methods an employee can use to get towork each day. Samples of times recorded for each method are shown. Times are in minutes.Public Transportation: 28 29 32 37 33 25 29 32 41 34 Automobile: 29 31 33 32 34 30 31 32 35 33a. Compute the sample mean
62. Small business owners often look to payroll service companies to handle their employee payroll. Reasons are that small business owners face complicated tax regulations and penalties for employment tax errors are costly. According to the Internal Revenue Service, 26% of all small business
61. The U.S. Department of Education reports that about 50% of all college students use a student loan to help cover college expenses (National Center for Educational Studies, January 2006). A sample of students who graduated with student loan debt is shown here.The data, in thousands of dollars,
60. Dividend yield is the annual dividend per share a company pays divided by the current market price per share expressed as a percentage. A sample of 10 large companies provided the following dividend yield data (The Wall Street Journal, January 16, 2004).
59. The U.S. Census Bureau provides statistics on family life in the United States, including the age at the time of first marriage, current marital status, and size of household(http://www.census.gov, March 20, 2006). The following data show the age at the time of first marriage for a sample of
58. According to the 2003 Annual Consumer Spending Survey, the average monthly Bank of America Visa credit card charge was $1838 (U.S. Airways Attaché Magazine, December 2003). A sample of monthly credit card charges provides the following data.236 1710 1351 825 7450 316 4135 1333 1584 387 991
57. The following frequency distribution shows the price per share for the 30 companies in the Dow Jones Industrial Average (The Wall Street Journal, January 16, 2006).
56. A survey of subscribers to Fortune magazine asked the following question: “How many of the last four issues have you read?” Suppose that the following frequency distribution summarizes 500 responses.a. What is the mean number of issues read by a Fortune subscriber?b. What is the standard
55. Bloomberg Personal Finance (July/August 2001) included the following companies in its recommended investment portfolio. For a portfolio value of $25,000, the recommended dollar amounts allocated to each stock are shown.a. Using the portfolio dollar amounts as the weights, what is the weighted
54. The grade point average for college students is based on a weighted mean computation.For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 9 credit hours of A, 15
53. Consider the sample data in the following frequency distribution.a. Compute the sample mean.b. Compute the sample variance and sample standard deviation.
52. Consider the following data and corresponding weights.a. Compute the weighted mean.b. Compute the sample mean of the four data values without weighting. Note the difference in the results provided by the two computations.
51. The daily high and low temperatures for 12 U.S. cities are as follows (Weather Channel, January 25, 2004).a. What is the sample mean daily high temperature?b. What is the sample mean daily low temperature?c. What is the correlation between the high and low temperatures?
50. The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 Index (S&P 500)are both used to measure the performance of the stock market. The DJIA is based on the price of stocks for 30 large companies; the S&P 500 is based on the price of stocks for 500 companies. If both the DJIA
49. PC World provided ratings for 15 notebook PCs (PC World, February 2000). The performance score is a measure of how fast a PC can run a mix of common business applications as compared to a baseline machine. For example, a PC with a performance score of 200 is twice as fast as the baseline
48. A department of transportation’s study on driving speed and mileage for midsize automobiles resulted in the following data.Driving Speed 30 50 40 55 30 25 60 25 50 55 Mileage 28 25 25 23 30 32 21 35 26 25 Compute and interpret the sample correlation coefficient.
47. Nielsen Media Research provides two measures of the television viewing audience: a television program rating, which is the percentage of households with televisions watching a program, and a television program share, which is the percentage of households watching a program among those with
46. Five observations taken for two variables follow.xi 6 11 15 21 27 yi 6 9 6 17 12a. Develop a scatter diagram for these data.b. What does the scatter diagram indicate about a relationship between x and y?c. Compute and interpret the sample covariance.d. Compute and interpret the sample
45. Five observations taken for two variables follow.xi 4 6 11 3 16 yi 50 50 40 60 30a. Develop a scatter diagram with x on the horizontal axis.b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?c. Compute and interpret the sample
44. A listing of 46 mutual funds and their 12-month total return percentage is shown in Table 3.6 (Smart Money, February 2004).a. What are the mean and median return percentages for these mutual funds?b. What are the first and third quartiles?c. Provide a five-number summary.d. Do the data contain
43. New York Stock Exchange (NYSE) Chairman Richard Grasso and NYSE Board of Directors came under fire for the large compensation package being paid to Grasso. When it comes to salary plus bonus, Grasso’s $8.5 million out-earned the top executives of all major financial services companies. The
42. Major League Baseball payrolls continue to escalate. Team payrolls in millions are as follows (USA Today Online Database, March 2006).a. What is the median team payroll?b. Provide a five-number summary.c. Is the $208 million payroll for the New York Yankees an outlier? Explain.d. Show a box
41. Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.8408 1374 1872 8879 2459 11413 608 14138 6452 1850 2818 1356 10498 7478 4019 4341 739 2127 3653 5794 8305a. Provide a five-number summary.b. Compute the lower and upper limits.c. Do the data contain any outliers?d.
40. Ebby Halliday Realtors provide advertisements for distinctive properties and estates located throughout the United States. The prices listed for 22 distinctive properties and estates are shown here (The Wall Street Journal,January 16, 2004). Prices are in thousands.1500 700 2995 895 619 880 719
39. A data set has a first quartile of 42 and a third quartile of 50. Compute the lower and upper limits for the corresponding box plot. Should a data value of 65 be considered an outlier?
38. Show the five-number summary and the box plot for the following data: 5, 15, 18, 10, 8, 12, 16, 10, 6.
37. Show the box plot for the data in exercise 36.
36. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Provide the fivenumber summary for the data.
35. Consumer Review posts reviews and ratings of a variety of products on the Internet. The following is a sample of 20 speaker systems and their ratings (http://www.audioreview.com).The ratings are on a scale of 1 to 5, with 5 being best.
34. A sample of 10 NCAA college basketball game scores provided the following data (USA Today, January 26, 2004).?
33. Florida Power & Light (FP&L) Company has enjoyed a reputation for quickly fixing its electric system after storms. However, during the hurricane seasons of 2004 and 2005, a new reality was that the company’s historical approach to emergency electric system repairs was no longer good enough
32. The high costs in the California real estate market have caused families who cannot afford to buy bigger homes to consider backyard sheds as an alternative form of housing expansion.Many are using the backyard structures for home offices, art studios, and hobby areas as well as for additional
31. The national average for the verbal portion of the College Board’s Scholastic Aptitude Test(SAT) is 507 (The World Almanac, 2006). The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped
30. The Energy Information Administration reported that the mean retail price per gallon of regular grade gasoline was $2.30 (Energy Information Administration, February 27, 2006).Suppose that the standard deviation was $.10 and that the retail price per gallon has a bellshaped distribution.a. What
29. The results of a national survey showed that on average, adults sleep 6.9 hours per night.Suppose that the standard deviation is 1.2 hours.a. Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours.b. Use Chebyshev’s theorem to calculate the
28. Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges.a. 20 to 40b. 15 to 45c. 25 to 35
27. Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges.a. 20 to 40b. 15 to 45c. 22 to 38d. 18 to 42e. 12 to 48
26. Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 520, 650, 500, 450, and 280?
25. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations.
24. The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes).Quarter-Mile Times: .92 .98 1.04 .90 .99 Mile Times: 4.52 4.35 4.60 4.70 4.50 After viewing this sample of running times, one of the coaches commented that the quartermilers
23. Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:2005 Season 74 78 79 77 75 73 75 77 2006 Season 71 70 75 77 85 80 71 79a. Use the mean and standard deviation to evaluate the golfer’s performance over the
22. The National Retail Federation reported that freshmen spend more on back-to-school items than any other college group (USA Today, August 4, 2006). Sample data comparing the back-to-school expenditures for 25 freshmen and 20 seniors are shown in the data file BackToSchool.a. What is the mean
21. How do grocery costs compare across the country? Using a market basket of 10 items including meat, milk, bread, eggs, coffee, potatoes, cereal, and orange juice, Where to Retire magazine calculated the cost of the market basket in six cities and in six retirement areas across the country (Where
20. The following data were used to construct the histograms of the number of days required to fill orders for Dawson Supply, Inc., and J.C. Clark Distributors (see Figure 3.2).Dawson Supply Days for Delivery: 11 10 9 10 11 11 10 11 10 10 Clark Distributors Days for Delivery: 8 10 13 7 10 11 10 7
19. The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50.a. Compute the range and interquartile range.b. Compute the sample variance
18. Car rental rates per day for a sample of seven Eastern U.S. cities are as follows (The Wall Street Journal, January 16, 2004).a. Compute the mean, variance, and standard deviation for the car rental rates.b. A similar sample of seven Western U.S. cities showed a sample mean car rental rate of
17. A home theater in a box is the easiest and cheapest way to provide surround sound for a home entertainment center. A sample of prices is shown here (Consumer Reports Buying Guide, 2004). The prices are for models with a DVD player and for models without a DVD player.
16. A bowler’s scores for six games were 182, 168, 184, 190, 170, and 174. Using these data as a sample, compute the following descriptive statistics.a. Rangec. Standard deviationb. Varianced. Coefficient of variation
15. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile range, variance, and standard deviation.
14. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the variance and standard deviation.
13. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range and interquartile range.
12. Walt Disney Company bought Pixar Animation Studios, Inc., in a deal worth $7.4 billion(CNNMoney.com, January 24, 2006). A list of the animated movies produced by Disney and Pixar during the previous 10 years follows. The box office revenues are in millions of dollars. Compute the total revenue,
11. In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance.City: 16.2 16.7 15.9 14.4 13.2 15.3 16.8 16.0 16.1 15.3 15.2 15.3 16.2 Highway:
10. A panel of economists provided forecasts of the U.S. economy for the first six months of 2007 (The Wall Street Journal, January 2, 2007). The percentage changes in gross domestic product (GDP) forecasted by 30 economists are as follows.2.6 3.1 2.3 2.7 3.4 0.9 2.6 2.8 2.0 2.4 2.7 2.7 2.7 2.9 3.1
9. J. D. Powers and Associates surveyed cell phone users in order to learn about the minutes of cell phone usage per month (Associated Press, June 2002). Minutes per month for a sample of 15 cell phone users are shown here.615 135 395 430 830 1180 690 250 420 265 245 210 180 380 105a. What is the
8. The cost of consumer purchases such as housing, gasoline, Internet services, tax preparation, and hospitalization were provided in The Wall Street Journal, January 2, 2007.Sample data typical of the cost of tax-return preparation by services such as H&R Block are shown here.120 230 110 115 160
7. The American Association of Individual Investors conducted an annual survey of discount brokers (AAII Journal, January 2003). The commissions charged by 24 discount brokers for two types of trades, a broker-assisted trade of 100 shares at $50 per share and an online trade of 500 shares at $50
6. The National Association of Colleges and Employers compiled information about annual starting salaries for college graduates by major. The mean starting salary for business administration graduates was $39,850 (CNNMoney.com, February 15, 2006). Samples with annual starting data for marketing
5. The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows:Atlanta $163 Minneapolis $125 Boston 177 New Orleans 167 Chicago 166 New York 245
4. Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the mean, median, and mode.
3. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 65th, and 75th percentiles.
2. Consider a sample with data values of 10, 20, 21, 17, 16, and 12. Compute the mean and median.
1. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the mean and median.
54. Refer to the data set in Table 2.17.a. Prepare a scatter diagram to show the relationship between the variables Market Value and Stockholders’ Equity.b. Comment on any relationship between the variables.
53. Refer to the data set in Table 2.17.a. Prepare a scatter diagram to show the relationship between the variables Profit and Stockholders’ Equity.b. Comment on any relationship between the variables.
52. Refer to the data set in Table 2.17.a. Prepare a crosstabulation for the variables Market Value and Profit.b. Compute the row percentages for your crosstabulation in part (a).c. Comment on any relationship between the variables.
51. Table 2.17 contains a portion of the data on the file named Fortune on the CD that accompanies the text. It provides data on stockholders’ equity, market value, and profits for a sample of 50 Fortune 500 companies.a. Prepare a crosstabulation for the variables Stockholders’ Equity and
50. A survey of commercial buildings served by the Cinergy-Cincinnati Gas & Electric Company asked what main heating fuel was used and what year the building was constructed. A partial crosstabulation of the findings follows.a. Complete the crosstabulation by showing the row totals and column
49. Do larger companies generate more revenue? The following data show the number of employees and annual revenue for a sample of 20 Fortune 1000 companies (Fortune, April 17, 2000).a. Prepare a scatter diagram to show the relationship between the variables Revenue and Employees.b. Comment on any
48. A study of job satisfaction was conducted for four occupations. Job satisfaction was measured using an 18-item questionnaire with each question receiving a response score of 1 to 5 with higher scores indicating greater satisfaction. The sum of the 18 scores provides the job satisfaction score
47. Refer to the data set for high and low temperatures for 20 cities in exercise 46.a. Develop a scatter diagram to show the relationship between the two variables, high temperature and low temperature.b. Comment on the relationship between high and low temperatures.
46. The daily high and low temperatures for 20 cities follow (USA Today, March 3, 2006).a. Prepare a stem-and-leaf display of the high temperatures.b. Prepare a stem-and-leaf display of the low temperatures.c. Compare the two stem-and-leaf displays and make comments about the difference between the
45. Drug Store News (September 2002) provided data on annual pharmacy sales for the leading pharmacy retailers in the United States. The following data are annual sales in millions.a. Show a stem-and-leaf display.b. Identify the annual sales levels for the smallest, medium, and largest drug
44. Data from the U.S. Census Bureau provides the population by state in millions of people(The World Almanac, 2006).a. Develop a frequency distribution, a percent frequency distribution, and a histogram.Use a class width of 2.5 million.b. Discuss the skewness in the distribution.c. What
43. Ninety-four shadow stocks were reported by the American Association of Individual Investors. The term shadow indicates stocks for small to medium-sized firms not followed closely by the major brokerage houses. Information on where the stock was traded—New York Stock Exchange (NYSE), American
42. Approximately 1.5 million high school students take the Scholastic Aptitude Test (SAT)each year and nearly 80% of the college and universities without open admissions policies use SAT scores in making admission decisions (College Board, March 2006). A sample of SAT scores for the combined math
41. Dividend yield is the annual dividend paid by a company expressed as a percentage of the price of the stock (Dividend/Stock Price 100). The dividend yield for the Dow Jones Industrial Average companies is shown in Table 2.16 (The Wall Street Journal, March 3, 2006).a. Construct a frequency
40. Golf Magazine’s Top 100 Teachers were asked the question, “What is the most critical area that prevents golfers from reaching their potential?” The possible responses were lack of accuracy, poor approach shots, poor mental approach, lack of power, limited practice, poor putting, poor
39. The Higher Education Research Institute at UCLA provides statistics on the most popular majors among incoming college freshmen. The five most popular majors are Arts and Humanities (A), Business Administration (B), Engineering (E), Professional (P), and Social Science (S) (The New York Times

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