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bayesian statistics an introduction
Statistics For Business And Economics 14th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann - Solutions
29. Cost Estimation Conclusion. 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 a = .05 to test whether the production volume is significantly
28. Broker Satisfaction Conclusion. In exercise 8, ratings data on x = the quality of the speed of execution and y = overall satisfaction with electronic trades provided the estimated regression equation yˆ = .2046 + .9077x. At the .05 level of significance, test whether speed of execution and
27. College GPA and Salary. Do students with higher college grade point averages (GPAs)earn more than those graduates with lower GPAs (CivicScience)? Consider the college GPA and salary data (10 years after graduation) provided in the file GPASalary.a. Develop a scatter diagram for these data with
26. Headphones Conclusion. In exercise 18, the data on price ($) and the overall score for six stereo headphones tested by Consumer Reports were as follows (Consumer Reports website).Brand Price ($) Score Bose 180 76 Skullcandy 150 71 Koss 95 61 Phillips/O’Neill 70 56 Denon 70 40 JVC 35 26a. Does
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 a = .05.c. Use the F test to test for a significant relationship. Use a = .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 (14.15).b. Compute the standard error of the estimate using equation (14.16).c. Compute the estimated standard deviation of b1 using equation (14.18).d. Use the t test to test the
23. The data from exercise 1 follow.xi 1 2 3 4 5 yi 3 7 5 11 14a. Compute the mean square error using equation (14.15).b. Compute the standard error of the estimate using equation (14.16).c. Compute the estimated standard deviation of b1 using equation (14.18).d. Use the t test to test the
22. Rental Car Revenue and Fleet Size. The following data were used to investigate the relationship between the number of cars in service (1000s) and the annual revenue($millions) for six smaller car rental companies (Auto Rental News website).Cars Revenue Company (1000s) ($ millions)U-Save Auto
21. Cost Estimation. 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
20. Price and Weight of Bicycles. Bicycling, the world’s leading cycling magazine, reviews hundreds of bicycles throughout the year. Their “Road-Race” category contains reviews of bikes used by riders primarily interested in racing. One of the most important factors in selecting a bike for
19. Sales Experience and Sales Performance. In exercise 7 a sales manager collected the following data on x = annual sales and y = years of experience. The estimated regression equation for these data is yˆ = 80 + 4x.Annual Years of Sales Salesperson Experience ($1000s)1 1 80 2 3 97 3 4 92 4 4 102
18. Price and Quality of Headphones. The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by Consumer Reports(Consumer Reports website). The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range
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 yˆ = 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
15. The data from exercise 1 follow.xi 1 2 3 4 5 yi 3 7 5 11 14 The estimated regression equation for these data is yˆ = .20 + 2.60x.a. Compute SSE, SST, and SSR using equations (14.8), (14.9), and (14.10).b. Compute the coefficient of determination r2. Comment on the goodness of fit.c. Compute
14. Distance and Absenteeism. A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (kilometers) between home and work for the employees.A sample of 10 employees was selected and the
13. Auditing Itemized Tax Deductions. 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 medi cal deductions, are more reasonable for taxpayers with large adjusted gross
12. Stock Beta. In June of 2016, Yahoo Finance reported the beta value for Coca-Cola was.82 (Yahoo Finance website). Betas for individual stocks are determined by simple linear regression. The dependent variable is the total return for the stock, and the independent variable is the total return for
11. Laptop Ratings. To help consumers in purchasing a laptop computer, Consumer Reports calculates an overall test score for each computer tested based upon rating factors such as ergonomics, portability, performance, display, and battery life. Higher overall scores indicate better test results.
10. Age and the Price of Wine. For a particular red wine, the following data show the auction price for a 750-milliliter bottle and the age of the wine in June of 2016(WineX website).Age (years) Price ($)36 256 20 142 29 212 33 255 41 331 27 173 30 209 45 297 34 237 22 182a. Develop a scatter
9. Estimating Landscaping Expenditures. David’s Landscaping has collected data on home values (in thousands of $) and expenditures (in thousands of $) on landscaping with the hope of developing a predictive model to help marketing to potential new clients. Data for 14 households may be found in
8. Broker Satisfaction. The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an
7. Sales Experience and Performance. A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons.Years of Annual Sales Salesperson Experience ($1000s)1 1 80 2 3 97 3 4 92 4 4 102 5 6 103 6 8 111 7 10
6. Passing and Winning in the NFL. The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the average number of passing yards per attempt (Yds/Att)
5. Production Line Speed and Quality Control. Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection
4. Retail and Trade: Female Managers. 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
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 = 6.
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 1 2 3 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
44. Defective Parts. A manufacturing company designed a factorial experiment to determine whether the number of defective parts produced by two machines differed and if the number of defective parts produced also depended on whether the raw material needed by each machine was loaded manually or by
43. Language Translation. A factorial experiment was designed to test for any significant differences in the time needed to translate other languages into English with two computerized language translators. Because the type of language translated was also considered a significant factor,
42. Golf Club Design. A major manufacturer of golf equipment is considering three designs for a new driver: Design A, Design B, and Design C. Each design differs slightly in terms of the material used to construct the driver’s head and shaft. The company would like to know if there is any
41. Late-Night Talk Show Viewership. Jimmy Kimmel Live! on ABC, The Tonight Show Starring Jimmy Fallon on NBC, and The Late Show with Stephen Colbert on CBS are three popular latenight talk shows. The following table shows the number of viewers in millions for a 10week period during the spring for
40. Fuel Efficiency of Gasoline Brands. A research firm tests the kilometersperliter characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the
39. Job Automation. A Pew Research study conducted in 2017 found that approximately 75% of Americans believe that robots and computers might one day do many of the jobs currently done by people (Pew Research website,
38. Assembly Methods. Three different assembly methods have been proposed for a new product. A completely randomized experimental design was chosen to determine which assembly method results in the greatest number of parts produced per hour, and 30 workers were randomly selected and assigned to use
37. College Attendance Rates. The following data show the percentage of 17to 24yearolds who are attending college in several metropolitan statistical areas in four geographic regions of the United States (U.S. Census Bureau website, https://www.census.gov/data.html).Northeast Midwest South West
36. Monitoring Air Pollution. The U.S. Environmental Protection Agency (EPA) monitors levels of pollutants in the air for cities across the country. Ozone pollution levels are measured using a 500point scale; lower scores indicate little health risk, and higher scores indicate greater health risk.
35. Job Satisfaction. A study reported in the Journal of Small Business Management concluded that selfemployed individuals do not experience higher job satisfaction than individuals who are not selfemployed.In this study, job satisfaction is measured using 18 items, each of which is rated using a
34. Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equalsize towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a .05 level of significance, does
33. Tax Research. A study reported in The Accounting Review examined the separate and joint effects of two levels of time pressure (low and moderate) and three levels of knowledge (naive, declarative, and procedural) on key word selection behavior in tax research. Subjects were given a tax case
32. Auto Fuel Efficiency. As part of a study designed to compare hybrid and similarly equipped conventional vehicles, Consumer Reports tested a variety of classes of hybrid and allgas model cars and sport utility vehicles (SUVs). The following data show the kilometersperliter rating Consumer
31. Amusement Park Queues. An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the
30. Mobile App Website Design. Based on a 2018 study, the average elapsed time between when a user navigates to a website on a mobile device until its main content is available was 14.6 seconds. This is more than a 20% increase from 2017(searchenginejournal.com,
29. The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST = 280, SSA = 26, SSB = 23, SSAB = 175. Set up the ANOVA table and test for any significant main effects and any interaction effect.
28. A factorial experiment involving two levels of factor A and three levels of factor B resulted in the following data.Factor B Level 1 Level 2 Level 3 Level 1 135 90 75 165 66 93 Factor A Level 2 125 127 120 95 105 136 Test for any significant main effects and any interaction. Use a = .05.
27. Consumer Preferences. In 2018, consumer goods giant Procter and Gamble (P&G)had more than 20 brands with more than $1 billion in annual sales (P&G website, https://us.pg.com/). How does a company like P&G create so many successful consumer products? P&G effectively invests in research and
26. SAT Performance. The Scholastic Aptitude Test (SAT) contains three areas: critical reading, mathematics, and writing. Each area is scored on an 800point scale. A sample of SAT scores for six students follows.Student Critical Reading Mathematics Writing 1 526 534 530 2 594 590 586 3 465 464 445
25. Airfares on Travel Websites. Are there differences in airfare depending on which travel agency website you utilize? The following data were collected on travel agency websites on July 9, 2018. The following table contains the prices in U.S. dollars for a oneway ticket between the cities listed
24. Auto Tune-Ups. An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tuneup depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tuneup time varies among compact, intermediate, and fullsized cars, the
23. An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table.Source of Variation Sum of Squares Degrees of Freedom Mean Square FTreatments 900 Blocks 400 Error Total 1800 Use a = .05 to test for any significant differences.
22. The following data were obtained for a randomized block design involving five treatments and three blocks: SST = 430, SSTR = 310, SSBL = 85. Set up the ANOVA table and test for any significant differences. Use a = .05.
21. Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table.Treatments A B C Blocks 1 10 9 8 2 12 6 5 3 18 15 14 4 20 18 18 5 8 7 8 Use a = .05 to test for any significant differences.
20. Minor League Baseball Attendance. The International League of TripleA minor league baseball consists of 14 teams organized into three divisions: North, South, and West. The following data show the average attendance for the 14 teams in the International League.Also shown are the teams’
19. Testing Time to Breakdown Between All Pairs of Machines. Refer to exercise 18.Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experimentwise error rate of .05 is desired.
18. Machine Breakdowns. To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained.Machine 1 Machine 2 Machine 3 Machine 4 6.4 8.7 11.1 9.9 7.8 7.4 10.3 12.8 5.3 9.4 9.7 12.1 7.4 10.1 10.3 10.8 8.4 9.2 9.2 11.3 7.3 9.8 8.8
17. Marketing Ethics. In the digital age of marketing, special care must be taken to make sure that programmatic ads appearing on websites align with a company’s strategy, culture and ethics. For example, in 2017, Nordstrom, Amazon and Whole Foods each faced boycotts form social media users when
16. Confidence Intervals for Different Processes. Refer to exercise 15. Use Fisher’s LSD procedure to develop a 95% confidence interval estimate of the difference between the means for manufacturer 1 and manufacturer 2.
15. Testing Chemical Processes. To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material.Manufacturer 1 2 3 20 28 20 26 26 19
14. The following data are from a completely randomized design. In the following calculations, use a = .05.Treatment 1Treatment 2Treatment 363 82 69 47 72 54 54 88 61 40 66 48 xj 51 77 58 s2j 96.67 97.34 81.99a. Use analysis of variance to test for a significant difference among the means of the
13. The following data are from a completely randomized design.Treatment ATreatment BTreatment C32 44 33 30 43 36 30 44 35 26 46 36 32 48 40 Sample mean 30 45 36 Sample variance 6.00 4.00 6.50a. At the a = .05 level of significance, can we reject the null hypothesis that the means of the three
12. Restaurant Satisfaction. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to fullservice restaurant chains (Consumer Reports website, https://www.consumerreports.org/cro/restaurants/buyingguide/index.htm). One of the variables in the study is meal price,
11. Paint-Drying Robots. How long it takes paint to dry can have an impact on the production capacity of a business. In May 2018, Deal’s Auto Body & Paint in Prescott, Arizona, invested in a paintdrying robot to speed up its process (The Daily Courier website,
10. Auditing Errors. Auditors must make judgments about various aspects of an audit on the basis of their own direct experience, indirect experience, or a combination of the two. In a study, auditors were asked to make judgments about the frequency of errors to be found in an audit. The judgments
9. Temperature’s Effect on a Chemical Process. To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels.The results follow. Construct an analysis of variance table. Use a .05 level of significance to test whether the
8. Testing Quality Awareness. Refer to the NCP data in Table 13.4. Set up the ANOVA table and test for any significant difference in the mean examination score for the three plants. Use a = .05.6
7. Product Assembly. Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each
6. Develop the analysis of variance computations for the following completely randomized design. At a = .05, is there a significant difference between the treatment means?Treatment A B C 136 107 92 120 114 82 113 125 85 107 104 101 131 107 89 114 109 117 129 97 110 102 114 120 104 98 89 106 xj 119
5. In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance. At a .05 level of significance, is there a significant difference between the treatments?Source of
4. In an experiment designed to test the output levels of three different treatments, the following results were obtained: SST = 400, SSTR = 150, nT = 19. Set up the ANOVA table and test for any significant difference between the mean output levels of the three treatments.Use a = .05.
3. Refer to exercise 2.a. What hypotheses are implied in this problem?b. At the a = .05 level of significance, can we reject the null hypothesis in part (a)?Explain.
2. In a completely randomized design, seven experimental units were used for each of the five levels of the factor. Complete the following ANOVA table.Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments 300 Error Total 460
1. The following data are from a completely randomized design.Treatment A B C 162 142 126 142 156 122 165 124 138 145 142 140 148 136 150 174 152 128 Sample mean 156 142 134 Sample variance 164.4 131.2 110.4a. Compute the sum of squares between treatments.b. Compute the mean square between
37. Testing If Daily Sales Obey a Binomial Probability Distribution. A salesperson makes four calls per day. A sample of 100 days gives the following frequencies of sales volumes.Number of Sales Observed Frequency(days)0 30 1 32 2 25 3 10 4 3 Total 100
36. Testing Normality of Final Exam Grades. A random sample of final examination grades for a college course follows.55 85 72 99 48 71 88 70 59 98 80 74 93 85 74 82 90 71 83 60 95 77 84 73 63 72 95 79 51 85 76 81 78 65 75 87 86 70 80 64 Use a = .05 and test to determine whether a normal probability
35. Best-Selling Small Cars in America. Based on 2017 sales, the six top-selling compact cars are the Honda Civic, Toyota Corolla, Nissan Sentra, Hyundai Elantra, Chevrolet Cruze, and Ford Focus (New York Daily News,
34. America’s Favorite Sports. The Harris Poll tracks the favorite sport of Americans who follow at least one sport. Results of the poll show that professional football is the favorite sport of 33% of Americans who follow at least one sport, followed by baseball at 15%, men’s college football
33. Attitudes Toward New Nuclear Power Plants. A Financial Times/Harris Poll surveyed people in six countries to assess attitudes toward a variety of alternate forms of energy. The data in the following table are a portion of the poll’s findings concerning whether people favor or oppose the
32. Ambulance Calls by Day of Week. An ambulance service responds to emergency calls for two counties in Virginia. One county is an urban county and the other is a rural county. A sample of 471 ambulance calls over the past two years showed the county and the day of the week for each emergency
31. Church Attendance by Age Group. The Barna Group conducted a survey about church attendance. The survey respondents were asked about their church attendance and asked to indicate their age. Use the sample data to determine whether church attendance is independent of age. Using a .05 level of
30. Pace-of-Life Preference By Gender. A Pew Research Center survey asked respondents if they would rather live in a place with a slower pace of life or a place with a faster pace of life. The survey also asked the respondent’s gender. Consider the following sample data.Gender Preferred Pace of
29. Ratings of Most-Visited Art Museums. As listed by The Art Newspaper Visitor Figures Survey (https://www.theartnewspaper.com/visitor-figures-2017), the five most-visited art museums in the world are the Louvre Museum, the National Museum in China, the Metropolitan Museum of Art, the Vatican
28. Quality Comparison Across Production Shifts. Arconic Inc. is a producer of aluminum components for the avionics and automotive industries. At its Davenport Works plant, an engineer has conducted a quality-control test in which aluminum coils produced in all three shifts were inspected. The
27. Where Millionaires Live in America. In a 2018 study, Phoenix Marketing International identified Bridgeport, Connecticut; San Jose, California; Washington, D.C.; and Lexington Park, Maryland as the four U.S. cities with the highest percentage of millionaires (Kiplinger website,
26. Weekly Demand at Whole Foods Market. The manager at a Whole Foods Market is responsible for managing store inventory. The mathematical models that she uses to determine how much inventory to stock rely on product demand being normally distributed.In particular, the weekly demand of sriracha
25. Daily High Temperatures. Bob Feller, an Iowa farmer, has recorded the daily high temperatures during the same five-day stretch in May over the past five years. Bob is interested in whether this data suggests that the daily high temperature obeys a normal distribution. Use a = .01 and conduct a
24. Traffic Accidents by Day of Week. The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of the week.Assume that a sample of 420 accidents provided the following data.Sunday Monday Tuesday Wednesday Thursday Friday Saturday 66 50 53 47
23. Shareholder Scoreboard Ratings. The Wall Street Journal’s Shareholder Scoreboard tracks the performance of 1000 major U.S. companies. The performance of each company is rated based on the annual total return, including stock price changes and the re investment of dividends. Ratings are
22. M&M Candy Colors. Mars, Inc. manufactures M&M’s, one of the most popular candy treats in the world. The milk chocolate candies come in a variety of colors including blue, brown, green, orange, red, and yellow. The overall proportions for the colors are .24 blue,.13 brown, .20 green, .16
21. Television Audiences Across Networks. During the first 13 weeks of the television season, the Saturday evening 8 p.m. to 9 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
20. The following data are believed to have come from a normal distribution. Use the goodness of fit test and a = .05 to test this claim.17 23 22 24 19 23 18 22 20 13 11 21 18 20 21 21 18 15 24 23 23 43 29 27 26 30 28 33 23 29 Applications
19. Test the following hypotheses by using the x2 goodness of fit test.H0:Ha:pA 5 .40, pB 5 .40, and pC 5 .20 The population proportions are not pA 5 .40, pB 5 .40, and pC 5 .20 A sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C.Use a = .01 and test to see
18. Movie Critic Opinions. On a television program, two movie critics provide their reviews of recent movies and discuss. It is suspected that these hosts deliberately disagree in order to make the program more interesting for viewers. Each movie review is categorized as Pro (“thumbs up”), Con
17. Amount of Sleep by Age Group. The National Sleep Foundation used a survey to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to
16. Academy Awards and Movie Fan Sentiment. The race for the 2013 Academy Award for Actress in a Leading Role was extremely tight, featuring several worthy performances. The nominees were Jessica Chastain for Zero Dark Thirty, Jennifer Lawrence for Silver Linings Playbook, Emmanuelle Riva for
15. Company Reputation and Management Quality Survey. The Wall Street Journal Annual Corporate Perceptions Study surveyed readers and asked how they rated the quality of management and the reputation of the company for more than 250 worldwide corporations. Both the quality of management and the
14. Vehicle Quality Ratings. A J. D. Power and Associates vehicle quality survey asked new owners a variety of questions about their recently purchased automobile. One question asked for the owner’s rating of the vehicle using categorical responses of average, outstanding, and exceptional.
13. Generational Differences in Workplace Attitudes. In 2015, Addison Group (a provider of professional staffing services) and Kelton (a global insights firm) surveyed the work preferences and attitudes of 1,006 working adults spread over three generations:baby boomers, Generation X, and
12. Hiring and Firing Plans at Private and Public Companies. A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: The company plans to hire and add to
10. The following table contains observed frequencies for a sample of 240. Test for independence of the row and column variables using a = .05.Column Variable Row Variable A B C P 20 30 20 Q 30 60 25 R 10 15 30a. Using a .05 level of significance, is the type of ticket purchased independent of the
9. The following table contains observed frequencies for a sample of 200. Test for independence of the row and column variables using a = .05.Column Variable Row Variable A B C P 20 44 50 Q 30 26 30
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