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essentials of statistics
Essentials Of Statistics For Business And Economics 5th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams - Solutions
5. The owner of Showtime Movie Theaters, Inc., would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.a. Develop an estimated regression equation with the amount of television advertising as the independent
4. A shoe store developed the following estimated regression equation relating sales to inventory investment and advertising expenditures.wherea. Estimate sales resulting from a $15,000 investment in inventory and an advertising budget of $10,000.b. Interpret b1 and b2 in this estimated regression
3. In a regression analysis involving 30 observations, the following estimated regression equation was obtained.a. Interpret b1, b2, b3, and b4 in this estimated regression equation.b. Estimate y when x1 10, x2 5, x3 1, and x4 2.
2. Consider the following data for a dependent variable y and two independent variables, x1 and x2.
1. The estimated regression equation for a model involving two independent variables and 10 observations follows.a. Interpret b1 and b2 in this estimated regression equation.b. Estimate y when x1 180 and x2 310.
60. The Australian Public Service Commission’s State of the Service Report 2002–2003 reported job satisfaction ratings for employees. One of the survey questions asked employees to choose the five most important workplace factors (from a list of factors) that most affected how satisfied they
59. The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service audit. The following table shows the average adjusted gross income reported and the percent of the returns that were audited for 20 selected IRS districts.
58. Bloomberg Personal Finance (July/August 2001) reported the market beta for Texas Instruments was 1.46. Market betas for individual stocks are determined by simple linear regression. For each stock, the dependent variable is its quarterly percentage return (capital appreciation plus dividends)
57. A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow.
56. The regional transit authority for a major metropolitan area wants to determine whether there is any relationship between the age of a bus and the annual maintenance cost. A sample of 10 buses resulted in the following data.
55. A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles)between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.
54. In a manufacturing process the assembly line speed (feet per minute) was thought to affect the number of defective parts found during the inspection process. To test this theory, managers devised a situation in which the same batch of parts was inspected visually at a variety of line speeds.
53. Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and
52. The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P) indexes are used as measures of overall movement in the stock market. The DJIA is based on the price movements of 30 large companies; the S&P 500 is an index composed of 500 stocks.Some say the S&P 500 is a better
51. Corporate share repurchase programs are often touted as a benefit for shareholders. But Robert Gabele, director of insider research for First Call/Thomson Financial, noted that many of these programs are undertaken solely to acquire stock for a company’s incentive options for top managers.
50. The data in the following table show the number of shares selling (millions) and the expected price (average of projected low price and projected high price) for 10 selected initial public stock offerings.a. Develop an estimated regression equation with the number of shares selling as the
49. American Depository Receipts (ADRs) are certificates traded on the NYSE representing shares of a foreign company held on deposit in a bank in its home country. The following table shows the price/earnings (P/E) ratio and the percentage return on investment(ROE) for 10 Indian companies that are
48. Refer to exercise 9, where an estimated regression equation relating years of experience and annual sales was developed.a. Compute the residuals and construct a residual plot for this problem.b. Do the assumptions about the error terms seem reasonable in light of the residual plot?
47. Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow.a. Let x equal advertising expenditures and y equal revenue. Use the method of least squares to develop a straight line approximation of the relationship between the two variables.b.
46. The following data were used in a regression studya. Develop an estimated regression equation for these data.b. Construct a plot of the residuals. Do the assumptions about the error term seem to be satisfied?
45. Given are data for two variables, x and y.xi 6 11 15 18 20 yi 6 8 12 20 30a. Develop an estimated regression equation for these data.b. Compute the residuals.c. Develop a plot of the residuals against the independent variable x. Do the assumptions about the error terms seem to be satisfied?
44. Cushman & Wakefield, Inc., collects data showing the office building vacancy rates and rental rates for markets in the United States. The following data show the overall vacancy rates (%) and the average rental rates (per square foot) for the central business district for 18 selected markets.
43. Health experts recommend that runners drink 4 ounces of water every 15 minutes they run.Although handheld bottles work well for many types of runs, all-day cross-country runs require hip-mounted or over-the-shoulder hydration systems. In addition to carrying more water, hip-mounted or
42. A regression model relating x, number of salespersons at a branch office, to y, annual sales at the office (in thousands of dollars) provided the following computer output from a regression analysis of the data.a. Write the estimated regression equation.b. How many branch offices were involved
41. Following is a portion of the computer output for a regression analysis relating y maintenance expense (dollars per month) to x usage (hours per week) of a particular brand of computer terminal.a. Write the estimated regression equation.b. Use a t test to determine whether monthly
40. The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the
39. Almost all U.S. light-rail systems use electric cars that run on tracks built at street level.The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The
38. Refer to Exercise 21, where data on the production volume x and total cost y for a particular manufacturing operation were used to develop the estimated regression equation 1246.67 7.6x.a. The company’s production schedule shows that 500 units must be produced next month. What is the point
37. In exercise 13, data were given on the adjusted gross income x and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regression equation 4.68 .16x, the point estimate of a reasonable level of total itemized deductions for a
36. In exercise 10, data on x temperature rating (F) and y price ($) for 11 sleeping bags manufactured by Bergans of Norway provided the estimated regression equation 359.2668 5.2772x. For these data s 37.9372.a. Develop a point estimate of the price for a sleeping bag with a temperature
35. In exercise 18, the data on grade point average x and monthly salary y provided the estimated regression equation 1790.5 581.1x.a. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA.b. Develop a 95% prediction interval for the starting salary for
34. The data from exercise 3 follow.xi 2 6 9 13 20 yi 7 18 9 26 23 Develop the 95% confidence and prediction intervals when x 12. Explain why these two intervals are different.
33. The data from exercise 2 follow.xi 3 12 6 20 14 yi 55 40 55 10 15a. Estimate the standard deviation of when x 8.b. Develop a 95% confidence interval for the expected value of y when x 8.c. Estimate the standard deviation of an individual value of y when x 8.d. Develop a 95% prediction
32. The data from exercise 1 follow.xi 123 4 5 yi 3 7 5 11 14a. Use equation (12.23) to estimate the standard deviation of when x 4.b. Use expression (12.24) to develop a 95% confidence interval for the expected value of y when x 4.
31. In exercise 20, data on x price ($) and y overall score for ten 42-inch plasma televisions tested by Consumer Reports provided the estimated regression equation 12.0169 .0127x. For these data SSE 540.04 and SST 982.40. Use the F test to determine whether the price for a 42-inch
30. Refer to exercise 22, where the following data were used to determine whether the price of a printer is related to the speed for plain text printing (PC World, February 2003).
29. Refer to exercise 21, where data on production volume and cost were used to develop an estimated regression equation relating production volume and cost for a particular manufacturing operation. Use α .05 to test whether the production volume is significantly related to the total cost. Show
28. In exercise 10, data on x temperature rating (F) and y price ($) for 11 sleeping bags manufactured by Bergans of Norway provided the estimated regression equation 359.2668 5.2772x. At the .05 level of significance, test whether temperature rating and price are related. Show the ANOVA
27. Outside Magazine tested 10 different models of day hikers and backpacking boots. The following data show the upper support and price for each model tested. Upper support was measured using a rating from 1 to 5, with a rating of 1 denoting average upper support and a rating of 5 denoting
26. In exercise 18 the data on grade point average and monthly salary were as follows.a. Does the t test indicate a significant relationship between grade point average and monthly salary? What is your conclusion? Use α .05.b. Test for a significant relationship using the F test. What is your
25. The data from exercise 3 follow.xi 2 6 9 13 20 yi 7 18 9 26 23a. What is the value of the standard error of the estimate?b. Test for a significant relationship by using the t test. Use α .05.c. Use the F test to test for a significant relationship. Use α .05. What is your conclusion?
24. The data from exercise 2 follow.xi 3 12 6 20 14 yi 55 40 55 10 15a. Compute the mean square error using equation (12.15).b. Compute the standard error of the estimate using equation (12.16).c. Compute the estimated standard deviation of b1 using equation (12.18).d. Use the t test to test the
23. The data from exercise 1 follow.xi 123 4 5 yi 3 7 5 11 14a. Compute the mean square error using equation (12.15).b. Compute the standard error of the estimate using equation (12.16).c. Compute the estimated standard deviation of b1 using equation (12.18).d. Use the t test to test the following
22. PC World provided ratings for the top five small-office laser printers and five corporate laser printers (PC World, February 2003). The highest rated small-office laser printer was the Minolta-QMS PagePro 1250W, with an overall rating of 91. The highest rated corporatea. Develop the estimated
21. An important application of regression analysis in accounting is in the estimation of cost.By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a
20. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following data show the price and overall score for the ten
19. The data from exercise 7 follow.The estimated regression equation for these data is 40,639 1301.2x. What percentage of the total sum of squares can be accounted for by the estimated regression equation?Comment on the goodness of fit. What is the sample correlation coefficient?
18. The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor’s degree in business administration with a major in information systems. The estimated regression equation for these data is yˆ 1790.5 581.1x.yˆyˆa. Compute SST, SSR, and
16. The data from exercise 2 follow.xi 3 12 6 20 14 yi 55 40 55 10 15 The estimated regression equation for these data is 68 3x.a. Compute SSE, SST, and SSR.b. Compute the coefficient of determination r2. Comment on the goodness of fit.c. Compute the sample correlation coefficient.17. The data
15. The data from exercise 1 follow.xi 123 4 5 yi 3 7 5 11 14 The estimated regression equation for these data is .20 2.60x.a. Compute SSE, SST, and SSR using equations (12.8), (12.9), and (12.10).b. Compute the coefficient of determination r2. Comment on the goodness of fit.c. Compute the
14. Starting salaries for accountants and auditors in Rochester, New York, trail those of many U.S. cities. The following data show the starting salary (in thousands of dollars) and the cost of living index for Rochester and nine other metropolitan areas (Democrat and Chronicle, September 1, 2002).
13. To the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer’s adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes.If a taxpayer claims larger
12. A personal watercraft (PWC) is a vessel propelled by water jets, designed to be operated by a person sitting, standing, or kneeling on the vessel. In the early 1970s, Kawasaki Motors Corp. U.S.A. introduced the JET SKI® watercraft, the first commercially successful PWC. Today, jet ski is
11. Although delays at major airports are now less frequent, it helps to know which airports are likely to throw off your schedule. In addition, if your plane is late arriving at a particular airport where you must make a connection, how likely is it that the departure will be late and thus
10. Bergans of Norway has been making outdoor gear since 1908. The following data show the temperature rating (F°) and the price ($) for 11 models of sleeping bags produced by Bergans(Backpacker 2006 Gear Guide).a. Develop a scatter diagram for these data with temperature rating (F°) as the
9. A sales manager collected the following data on annual sales and years of experience.a. Develop a scatter diagram for these data with years of experience as the independent variable.b. Develop an estimated regression equation that can be used to predict annual sales given the years of
8. According to Advertising Age’s annual salary review, Mark Hurd, the 49-year-old chairman, president, and CEO of Hewlett-Packard Co., received an annual salary of $817,000, a bonus of more than $5 million, and other compensation exceeding $17 million. His total compensation was slightly better
7. Would you expect more reliable cars to cost more? Consumer Reports rated 15 upscale sedans. Reliability was rated on a 5-point scale: poor (1), fair (2), good (3), very good (4), and excellent (5). The price and reliability rating for each of the 15 cars are shown (Consumer Reports, February
6. The following data show the annual advertising expenditure in millions of dollars and the market share for six automobile companies (Advertising Age, June 23, 2006).a. Develop a scatter diagram for these data with the advertising expenditure as the independent variable and the market share as
5. Technological advances helped make inflatable paddlecraft suitable for backcountry use.These blow-up rubber boats, which can be rolled into a bundle not much bigger than a golf bag, are large enough to accommodate one or two paddlers and their camping gear. Canoe &Kayak magazine tested boats
4. The following data give the percentage of women working in five companies in the retail and trade industry. The percentage of management jobs held by women in each company is also shown.% Working 67 45 73 54 61% Management 49 21 65 47 33a. Develop a scatter diagram for these data with the
3. Given are five observations collected in a regression study on two variables.xi 2 6 9 13 20 yi 7 18 9 26 23a. Develop a scatter diagram for these data.b. Develop the estimated regression equation for these data.c. Use the estimated regression equation to predict the value of y when x 4.
2. Given are five observations for two variables, x and y.xi 3 12 6 20 14 yi 55 40 55 10 15a. Develop a scatter diagram for these data.b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?c. Try to approximate the relationship between x
1. Given are five observations for two variables, x and y.xi 123 4 5 yi 3 7 5 11 14a. Develop a scatter diagram for these data.b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?c. Try to approximate the relationship between x and y by
45. A salesperson makes four calls per day. A sample of 100 days gives the following frequencies of sales volumes.Records show sales are made to 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial distribution. The binomial probability
44. The office occupancy rates were reported for four California metropolitan areas. Do the following data suggest that the office vacancies were independent of metropolitan area?Use a .05 level of significance. What is your conclusion?
43. Barna Research Group collected data showing church attendance by age group (USA Today, November 20, 2003). Use the sample data to determine whether attending church is independent of age. Use a .05 level of significance. What is your conclusion? What conclusion can you draw about church
42. Data on the marital status of men and women ages 20 to 29 were obtained as part of a national survey. The results from a sample of 350 men and 400 women follow.a. Use α .01 and test for independence between marital status and gender. What is your conclusion?b. Summarize the percent in each
41. A lending institution supplied the following data on loan approvals by four loan officers.Use α .05 and test to determine whether the loan approval decision is independent of the loan officer reviewing the loan application.
40. The Wall Street Journal Subscriber Study showed data on the employment status of subscribers. Sample results corresponding to subscribers of the eastern and western editions are shown here.Use α .05 and test the hypothesis that employment status is independent of the region.What is your
39. A sample of parts provided the following contingency table data on part quality by production shift.Use α .05 and test the hypothesis that part quality is independent of the production shift.What is your conclusion?
38. The results of Computerworld’s Annual Job Satisfaction Survey showed that 28% of information systems (IS) managers are very satisfied with their job, 46% are somewhat satisfied, 12% are neither satisfied nor dissatisfied, 10% are somewhat dissatisfied, and 4% are very dissatisfied. Suppose
37. A regional transit authority is concerned about the number of riders on one of its bus routes.In setting up the route, the assumption is that the number of riders is the same on every day from Monday through Friday. Using the following data, test with α .05 to determine whether the transit
36. Since 2000, the Toyota Camry, Honda Accord, and Ford Taurus have been the three bestselling passenger cars in the United States. Sales data for 2003 indicated market shares among the top three as follows: Toyota Camry 37%, Honda Accord 34%, and Ford Taurus 29% (The World Almanac, 2004). Assume
35. Seven percent of mutual fund investors rate corporate stocks “very safe,” 58% rate them“somewhat safe,” 24% rate them “not very safe,” 4% rate them “not at all safe,” and 7%are “not sure.” A BusinessWeek/Harris poll asked 529 mutual fund investors how they would rate
34. In setting sales quotas, the marketing manager makes the assumption that order potentials are the same for each of four sales territories. A sample of 200 sales follows. Should the manager’s assumption be rejected? Use α .05.Supplementary Exercises 455 Sales Territories I II III IV 60 45
33. In June 2001, 38% of fund managers surveyed believed that the core inflation rate would be higher in one year. One month later a similar survey revealed that 22% of fund managers expected the core inflation rate to be higher in one year (Global Research Highlights, Merrill Lynch, July 20,
32. In July 2001, the Harris Ad Track Research Service conducted a survey to evaluate the effectiveness of a major advertising campaign for Kodak cameras (USA Today, August 27, 2001). In a sample of 430 respondents, 163 thought the ads were very effective. In another sample of 285 respondents to
31. Medical tests were conducted to learn about drug-resistant tuberculosis. Of 142 cases tested in New Jersey, 9 were found to be drug-resistant. Of 268 cases tested in Texas, 5 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of
30. A large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period.a. Use α .05. Test to determine whether the claim rates differ between single and married male
29. Jupiter Media used a survey to determine how people use their free time. Watching television was the most popular activity selected by both men and women (The Wall Street Journal, January 26, 2004). The proportion of men and the proportion of women who selected watching television as their most
28. Samples taken in three cities,Anchorage,Atlanta, and Minneapolis, were used to learn about the percentage of married couples with both the husband and the wife in the workforce(USA Today,January 15, 2006). Analyze the following data to see whether both the husband and wife being in the
27. The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and
26. Businesses are increasingly placing orders online. The Performance Measurement Group collected data on the rates of correctly filled electronic orders by industry (Investor’s Business Daily, May 8, 2000).Assume a sample of 700 electronic orders provided the following results.a. Test a
25. FlightStats, Inc., collects data on the number of flights scheduled and the number of flights flown at major airports throughout the United States. FlightStats data showed 56% of flights scheduled at Newark, La Guardia, and Kennedy airports were flown during a threeday snowstorm (The Wall
24. A State of Washington’s Public Interest Research Group (PIRG) study showed that 46%of full-time college students work 25 or more hours per week. The PIRG study provided data on the effects of working on grades (USA Today,April 17, 2002). A sample of 200 students included 90 who worked 1–15
23. With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (USA Today, January 23, 2004).The following sample data provide a comparison of workers with and without health insurance coverage for small, medium,
22. Visa Card USA studied how frequently consumers of various age groups use plastic cards(debit and credit cards) when making purchases (Associated Press, January 16, 2006).Sample data for 300 customers shows the use of plastic cards by four age groups.
21. One of the questions on the BusinessWeek Subscriber Study was, “In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?” The data obtained are shown in the following contingency table.Use α .05 and test for the independence of type of
20. The following 3 3 contingency table contains observed frequencies for a sample of 240.Test for independence of the row and column variables using the 2 test with α .05.
19. The following 2 3 contingency table contains observed frequencies for a sample of 200.Test for independence of the row and column variables using the 2 test with α .05.
18. How well do airline companies serve their customers? A study showed the following customer ratings: 3% excellent, 28% good, 45% fair, and 24% poor (BusinessWeek, September 11, 2000). In a follow-up study of service by telephone companies, assume that a sample of 400 adults found the following
17. The Wall Street Journal’s Shareholder Scoreboard tracks the performance of 1000 major U.S. companies (The Wall Street Journal, March 10, 2003). The performance of each company is rated based on the annual total return, including stock price changes and the reinvestment of dividends. Ratings
16. The American Bankers Association collects data on the use of credit cards, debit cards, personal checks, and cash when consumers pay for in-store purchases (The Wall Street Journal, December 16, 2003). In 1999, the following usages were reported.
15. Where do women most often buy casual clothing? Data from the U.S. Shopper Database provided the following percentages for women shopping at each of the various outlets (The Wall Street Journal, January 28, 2004).The other category included outlets such as Target, Kmart, and Sears as well as
14. M&M/MARS, makers of M&M® Chocolate Candies, conducted a national poll in which more than 10 million people indicated their preference for a new color. The tally of this poll resulted in the replacement of tan-colored M&Ms with a new blue color. In the brochure “Colors,” made available by
13. During the first 13 weeks of the television season, the Saturday evening 8:00 p.m. to 9:00 p.m. audience proportions were recorded as ABC 29%, CBS 28%, NBC 25%, and independents 18%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience
12. Suppose we have a multinomial population with four categories: A, B, C, and D. The null hypothesis is that the proportion of items is the same in every category. The null hypothesis is A sample of size 300 yielded the following results.Use α .05 to determine whether H0 should be rejected.
11. Test the following hypotheses by using the 2 goodness of fit test.A sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C.Use α .01 and test to see whether the proportions are as stated in H0.a. Use the p-value approach.b. Repeat the test using the critical
10. During the 2003 Super Bowl, Miller Lite Beer’s commercial referred to as “The Miller Lite Girls” ranked among the top three most effective advertisements aired during the Super Bowl (USA Today, December 29, 2003). The survey of advertising effectiveness, conducted by USA Today’s Ad
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