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business
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
65. Scholarship Examination Scores. At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical population standard deviation s = 180 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the
64. Production Line Fill Weights. A production line operates with a mean filling weight of 450 grams per container. Overfilling or underfilling presents a serious problem and when detected requires the operator to shut down the production line to readjust the filling mechanism. From past data, a
63. GPS Usage in Canada. According to CNN, 55% of all U.S. smartphone users have used their GPS capability to get directions. Suppose a major provider of wireless telephone service in Canada wants to know how GPS usage by its customers compares with U.S. smartphone users. The company collects usage
62. French Fry Purchases. The American Potato Growers Association (APGA) would like to test the claim that the proportion of fast-food orders this year that include French fries exceeds the proportion of fast-food orders that included French fries last year. Suppose that a random sample of 49,581
61. CEOs and Social Networks. CEOs who belong to a popular business-oriented social networking service have an average of 930 connections. Do other members have fewer connections than CEOs? The number of connections for a random sample of 7,515 members who are not CEOs is provided in the file
60. Governmental Use of email. The Federal Government wants to determine if the mean number of business emails sent and received per business day by its employees differs from the mean number of emails sent and received per day by corporate employees, which is 101.5. Suppose the department
59. Automobile Mileage. An automobile mileage study tested the following hypotheses.Hypothesis Conclusion H0: m ≥ 10.6 km/L Manufacturer’s claim supported Ha: m < 10.6 km/L Manufacturer’s claim rejected; average kilometers per liter less than stated For s = 1.3 and a .02 level of
58. Mean Age of Magazine Subscribers. Young Adult magazine states the following hypotheses about the mean age of its subscribers.H0:Ha:m 5 28 m ± 28 If the manager conducting the test will permit a .15 probability of making a Type II error when the true mean age is 29, what sample size should be
57. Battery Life. A special industrial battery must have a life of at least 400 hours. A hypothesis test is to be conducted with a .02 level of significance. If the batteries from a particular production run have an actual mean use life of 385 hours, the production manager wants a sampling
56. Underfilling Packages of Coffee. Suppose the project director for the Hilltop Coffee study (see Section 9.3) asked for a .10 probability of claiming that Hilltop was not in violation when it really was underfilling by 25 grams (ma = 1.335 kilograms). What sample size would have been recommended?
54. Consider the following hypothesis test.H0:Ha:m $ 10 m , 10 The sample size is 120 and the population standard deviation is 5. Use a = .05. If the actual population mean is 9, the probability of a Type II error is .2912. Suppose the researcher wants to reduce the probability of a Type II error
53. Employee Participation in Investment Plans. Sparr Investments, Inc., specializes in tax-deferred investment opportunities for its clients. Recently Sparr offered a payroll deduction investment program for the employees of a particular company. Sparr estimates that the employees are currently
52. Length of Telephone Surveys. Refer to exercise 48. Assume the firm selects a sample of 50 surveys and repeat parts (b) and (c). What observation can you make about how increasing the sample size affects the probability of making a Type II error?
51. Production Line Accuracy. A production line operation is tested for filling weight accuracy using the following hypotheses.Hypothesis Conclusion and Action H0: m = 16 Filling okay; keep running Ha: m Þ 16 Filling off standard; stop and adjust machine The sample size is 30 and the population
50. Age of Magazine Subscribers. Young Adult magazine states the following hypotheses about the mean age of its subscribers.H0:Ha:m 5 28 m ± 28a. What would it mean to make a Type II error in this situation?b. The population standard deviation is assumed known at s = 6 years and the sample size is
49. Kilometers per Liter. A consumer research group is interested in testing an automobile manufacturer’s claim that a new economy model will travel at least 10.6 kilometers per liter of gasoline (H0: m $ 10.6).a. With a .02 level of significance and a sample of 30 cars, what is the rejection
48. Length of Telephone Surveys. Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed within 15 minutes or less. If more time is required, a premium rate is charged. With a sample of 35 surveys, a population standard deviation of 4
47. Consider the following hypothesis test.H0:Ha:m 5 20 m ± 20 A sample of 200 items will be taken and the population standard deviation is s = 10.Use a = .05. Compute the probability of making a Type II error if the population mean is:a. m = 18.0b. m = 22.5c. m = 21.0
46. Consider the follow ing hypothesis test.H0:Ha:m $ 10 m , 10 The sample size is 120 and the population standard deviation is assumed known with s = 5. Use a = .05.a. If the population mean is 9, what is the probability that the sample mean leads to the conclusion do not reject H0?b. What type of
45. Bullish, Neutral, or Bearish. The American Association of Individual Investors conducts a weekly survey of its members to measure the percent who are bullish, bearish, and neutral on the stock market for the next six months. For the week ending November 7, 2012, the survey results showed 35.0%
44. Malpractice Suits. One of the reasons health care costs have been rising rapidly in recent years is the increasing cost of malpractice insurance for physicians. Also, fear of being sued causes doctors to run more precautionary tests (possibly unnecessary)just to make sure they are not guilty of
43. Coupon Usage. Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the
42. Returned Merchandise. According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets returned. A Houston department store sampled 80 items sold in January and found that 12 of the items were returned.a. Construct a point estimate of
41. Adequate Preparation for Retirement. In 2018, RAND Corporation researchers found that 71% of all individuals ages 66 to 69 are adequately prepared financially for retirement. Many financial planners have expressed concern that a smaller percentage of those in this age group who did not complete
40. Holiday Gifts from Employers. Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 35% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners.a.
39. Population Mobility. What percentage of the population live in their state of birth?According to the U.S. Census Bureau’s 2014 American Community Survey, the figure ranges from 25% in Nevada to 78.7% in Louisiana. The average percentage across all states and the District of Columbia is 57.7%.
38. Attitudes toward Supermarket Brands. A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a
37. Union Membership. The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belonged to unions in 2013. Suppose a sample of 400 U.S. workers is collected in 2018 to determine whether union efforts to organize have increased union membership.a. Formulate the hypotheses that can be
36. Consider the following hypothesis test:H0:Ha:p $ .75 p , .75 A sample of 300 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use a = .05.a. p = .68c. p = .70b. p = .72d. p = .77
35. Consider the following hypothesis test:H0:Ha:p 5 .20 p ± .20 A sample of 400 provided a sample proportion p = .175.a. Compute the value of the test statistic.b. What is the p-value?c. At a = .05, what is your conclusion?d. What is the rejection rule using the critical value? What is your
34. Landscaping Labor Costs. Joan’s Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating
33. Automobile Insurance Premiums. The Onsure.com website reports that the mean annual premium for automobile insurance in the United States was $1503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support
32. Used Car Prices. According to the National Automobile Dealers Association, the mean price for used cars is $10,192. A manager of a Kansas City used car dealership reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether the population mean price for
31. Chocolate Consumption. The United States ranks ninth in the world in per capita chocolate consumption; Forbes reports that the average American eats 4.32 kilograms of chocolate annually. Suppose you are curious whether chocolate consumption is higher in Hershey, Pennsylvania, the location of
30. Time in Child Care. The time married men with children spend on child care averages 6.4 hours per week. You belong to a professional group on family practices that would like to do its own study to determine if the time married men in your area spend on child care per week differs from the
29. Cost of Residential Water. On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the residential water rates of other U.S. public utilities compare to Tulsa's rate? The file ResidentialWater contains the rate per 5 CCF of
28. CEO Tenure. A shareholders’ group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x = 7.27 years for CEOs with a standard deviation of s =
27. Price of Good Red Wine. According to the Vivino website, the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England–based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it
25. Consider the following hypothesis test:H0:Ha:m $ 45 m , 45 A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use a = .01.a. x = 44 and s = 5.2b. x = 43 and s = 4.6c. x = 46 and s = 5.0 26. Consider the following hypothesis
24. Consider the following hypothesis test:H0:Ha:m 5 18 m ± 18 A sample of 48 provided a sample mean x = 17 and a sample standard deviation s = 4.5.a. Compute the value of the test statistic.b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value.c. At a = .05,
23. Consider the following hypothesis test:H0:Ha:m # 12 m . 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.32.a. Compute the value of the test statistic.b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value.c. At a = .05,
22. Time in Supermarket Checkout Lines. CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a
21. Cost of Telephone Surveys. Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged.A sample of 35 surveys provided the survey
20. Prescription Drug Costs. Annual expenditure for prescription drugs was $838 per person in the Northeast of the country. A sample of 60 individuals in the Midwest showed a per person annual expenditure for prescription drugs of $745. Use a population standard deviation of $300 to answer the
19. Length of Calls to the IRS. According to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callers who placed their calls to the IRS
18. CPA Work Hours. The American Institute of Certified Tax Planners reports that the average U.S. CPA works 60 hours per week during tax season. Do CPAs in states that have flat state income tax rates work fewer hours per week during tax season? Conduct a hypothesis test to determine if this is
17. Use of Texting. TextRequest reports that adults 18–24 years old send and receive 128 texts every day. Suppose we take a sample of 25–34 year olds to see if their mean number of daily texts differs from the mean for 18–24 year olds reported by TextRequest.a. State the null and alternative
16. Credit Card Use by Undergraduates. In a study entitled How Undergraduate Students Use Credit Cards, it was reported that undergraduate students have a mean credit card balance of $3173. This figure was an all-time high and had increased 44% over the previous five years. Assume that a current
15. Federal Tax Returns. According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1056 in 2018. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically
14. Consider the following hypothesis test:H0:Ha:m 5 22 m ± 22 A sample of 75 is used and the population standard deviation is 10. Compute the p-value and state your conclusion for each of the following sample results. Use a = .01.a. x = 23b. x = 25.1c. x = 20
13. Consider the following hypothesis test:H0:Ha:m # 50 m . 50 A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use a = .05.a. x = 52.5b. x = 51c. x = 51.8
12. Consider the following hypothesis test:H0:Ha:m $ 80 m , 80 A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use a = .01.a. x = 78.5b. x = 77c. x = 75.5d. x = 81
11. Consider the following hypothesis test:H0:Ha:m 5 15 m ± 15 A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3.a. Compute the value of the test statistic.b. What is the p-value?c. At a = .05, what is your conclusion?d. What is the rejection rule using the
10. Consider the following hypothesis test:H0:Ha:m # 25 m . 25 A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.a. Compute the value of the test statistic.b. What is the p-value?c. At a = .01, what is your conclusion?d. What is the rejection rule using the
9. Consider the following hypothesis test:H0:Ha:m $ 20 m , 20 A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.a. Compute the value of the test statistic.b. What is the p-value?c. Using a = .05, what is your conclusion?d. What is the rejection rule using the
8. Production Operating Costs. Suppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour.a. State the appropriate null and alternative hypotheses if the mean cost for the current production method is
7. Carpet Salesperson Salaries. Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm’s vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation
6. Orange Juice Labels. The label on a 3-liter container of orange juice states that the orange juice contains an average of 1 gram of fat or less. Answer the following questions for a hypothesis test that could be used to test the claim on the label.a. Develop the appropriate null and alternative
5. Beer and Cider Consumption. According to the National Beer Wholesalers Association, U.S. consumers 21 years and older consumed 101.7 liters of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers
4. Process Improvement. Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $220 per hour. A
3. Filling Detergent Cartons. A production line operation is designed to fill cartons with laundry detergent to a mean weight of 900 grams. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion
2. Bonus Plan's Effect on Automobile Sales. The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan
1. Hotel Guest Bills. The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of
68. Structurally Deficient Bridges. The Infrastructure Report Card (IRC) reports that of 614,387 U.S. bridges, 9.1% were structurally deficient as of last year. The IRC also reports that more than 1300 California bridges fall under this category. How does California compare to the nation? Consider
67. FTC Fraud Reports. In 2017, 42.54% of the nearly 2.7 million reports taken nationwide by the Federal Trade Commission’s Consumer Sentinel Network dealt with instances of fraud. Consider results of a random sample of 42,296 of the reports taken by the Consumer Sentinel Network from Florida
66. Underemployment. A recent survey from PayScale found that 46% of U.S. workers—roughly 22 million—are underemployed, either working parttime or at jobs that don’t allow them to use their education or skills. Suppose that the numbers of hours worked in the past week were collected from a
65. Driving Speeds. Huston Systems Private Limited reports that smart traffic signals and signs can measure a passing vehicle’s speed. Consider the speeds of 15,717 vehicles collected as they passed 55 km/h speed limit signs throughout the United States in 2018 that are provided in the file
64. Factors in Choosing an Airline. Although airline schedules and cost are important factors for business travelers when choosing an airline carrier, a USA Today survey found that business travelers list an airline’s frequent flyer program as the most important factor. From a sample of n = 1993
63. Credit Card Ownership. Credit card ownership varies across age groups. In 2018, CreditCards.com estimated that the percentage of people who own at least one credit card is 67% in the 18–24 age group, 83% in the 25–34 age group, 76% in the 35–49 age group, and 78% in the 50+ age group.
62. Credit Card Balances. A wellknown bank credit card firm wishes to estimate the proportion of credit card holders who carry a nonzero balance at the end of the month and incur an interest charge. Assume that the desired margin of error is .03 at 98%confidence.a. How large a sample should be
61. Smoking. In 2014, the Centers for Disease Control reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30.a. How large a sample should be
60. Importance of Economy to Voters. A survey of 750 likely voters in Ohio was conducted by the Rasmussen Poll just prior to the general election. The state of the economy was thought to be an important determinant of how people would vote. Among other things, the survey found that 165 of the
59. Social Media Usage. The Pew Research Center has conducted extensive research on social media usage. One finding, reported in June 2018, was that 78% of adults aged 18 to 24 use Snapchat. Another finding was that 45% of those aged 18 to 24 use Twitter.Assume the sample size associated with both
58. Parenting Time. A USA Today/CNN/Gallup survey of 369 working parents found 200 who said they spend too little time with their children because of work commitments.a. What is the point estimate of the proportion of the population of working parents who feel they spend too little time with their
57. Paying for College Tuition. The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study.a. Provide a 95% confidence interval for the population proportion of
56. CEO Compensation. Annual salary plus bonus data for chief executive officers are presented in the BusinessWeek Annual Pay Survey. A preliminary sample showed that the standard deviation is $675 with data provided in thousands of dollars. How many chief executive officers should be in a sample
55. Patient Treatment Time. In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient.How large a sample should be taken if the desired margin of error is two minutes at a 95% level of confidence? How large a sample
54. Automobile Tests. Tests are conducted for a particular model of automobile. If a 98%confidence interval with a margin of error of 0.4 kilometer per liter is desired, how many automobiles should be used in the test? Assume that preliminary tests indicate the standard deviation is 1 kilometer per
53. Obesity. Obesity is a risk factor for many health problems such as type 2 diabetes, high blood pressure, joint problems, and gallstones. Using data collected in 2018 through the National Health and Nutrition Examination Survey, the National Institute of Diabetes and Digestive and Kidney
52. Health Care Expenditures. The Health Care Cost Institute tracks health care expenditures for beneficiaries under the age of 65 who are covered by employersponsored private health insurance. The data contained in the file DrugCost are consistent with the institute’s findings concerning annual
51. Healthy Sleep Duration. The Centers for Disease Control and Prevention (CDC)define a healthy sleep duration to be at least seven hours per day. The CDC reports that the percentage of people who report a healthy sleep duration varies by marital status. The CDC also reports that in 2018, 67% of
50. Annual Restaurant Expenditures. The 92 million Americans of age 50 and over control 50 percent of all discretionary income. AARP estimates that the average annual expenditure on restaurants and carryout food was $1873 for individuals in this age group. Suppose this estimate is based on a sample
49. Family Vacation Expenses. A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day while on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls resulted in a sample mean of $252.45 per day and a sample
48. Discount Brokerage Trade Fees. A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77. The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.a. Using the
47. Speeding Drivers. In 2017, ABC News reported that 58% of U.S. drivers admit to speeding. Suppose that a new satellite technology can instantly measure the speed of any vehicle on a U.S. road and determine whether the vehicle is speeding, and this satellite technology was used to take a sample
46. Web Browser Satisfaction. Internet users were recently asked online to rate their satisfaction with the web browser they use most frequently. Of 102,519 respondents, 65,120 indicated they were very satisfied with the web browser they use most frequently.a. What is the sample proportion of
45. Federal Government Employee Sick Hours. According to the Census Bureau, 2,475,780 people are employed by the federal government in the United States as of 2018. Suppose that a random sample of 3,500 of these federal employees was selected and the number of sick hours each of these employees
44. Federal Tax Return Errors. Suppose a sample of 10,001 erroneous Federal income tax returns from last year has been taken and is provided in the file FedTaxErrors. A positive value indicates the taxpayer underpaid and a negative value indicates that the taxpayer overpaid.a. What is the sample
43. Internet Usage. The Pew Research Center Internet Project, conducted in 2014 on the 25th anniversary of the Internet, involved a survey of 857 Internet users. It provided a variety of statistics on Internet users. For instance, in 2014, 87% of American adults were Internet users. In 1995 only
42. Voter Intent. A poll for the presidential campaign sampled 491 potential voters in June. A primary purpose of the poll was to obtain an estimate of the proportion of potential voters who favored each candidate. Assume a planning value of p* = .50 and a 95% confidence level.a. For p* = .50, what
41. Driver’s License Rates. Fewer young people are driving. In 1995, 63.9% of people under 20 years old who were eligible had a driver’s license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample of 1200 people under 20 years old
40. Employee Contributions to Health-Care Coverage. For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent survey
39. Stay-at-Home Parenting. In June 2014, Pew Research reported that in 16% of all homes with a stayathome parent, the father is the stayathome parent. An independent research firm has been charged with conducting a sample survey to obtain more current information.a. What sample size is needed if
38. Franchise Profits. According to Franchise Business Review, over 50% of all food franchises earn a profit of less than $50,000 a year. In a sample of 142 casual dining restaurants, 81 earned a profit of less than $50,000 last year.a. What is the point estimate of the proportion of casual dining
37. Voter Sentiment. One of the questions Rasmussen Reports included on a 2018 survey of 2.500 likely voters asked if the country is headed in the right direction. Representative data are shown in the file RightDirection. A response of Yes indicates that the respondent does think the country is
36. Automobile Insurance Coverage. According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the CNBC report, showed 46 of 200 vehicles were not covered by insurance.a. What is the point estimate of the proportion
35. Health-Care Survey. In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1007 adults to learn about their major healthcare concerns.The survey results showed that 574 of the respondents lack confidence they will be able to afford health insurance in the
34. At 95% confidence, how large a sample should be taken to obtain a margin of error of.03 for the estimation of a population proportion? Assume that past data are not available for developing a planning value for p*.
33. In a survey, the planning value for the population proportion is p* = .35. How large a sample should be taken to provide a 95% confidence interval with a margin of error of .05?
32. A simple random sample of 800 elements generates a sample proportion p = .70.a. Provide a 90% confidence interval for the population proportion.b. Provide a 95% confidence interval for the population proportion.
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