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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
31. A simple random sample of 400 individuals provides 100 Yes responses.a. What is the point estimate of the proportion of the population that would provide Yes responses?b. What is your estimate of the standard error of the proportion, sp?c. Compute the 95% confidence interval for the population
30. Kilometers Driven by Young Drivers. There has been a trend toward less driving in the last few years, especially by young people. Over the past eight years, the annual vehicle kilometers traveled by people from 16 to 34 years of age decreased from 16,580 to 12,720 kilometers per person. Assume
29. Length of Theater Previews. Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The
28. Beef Consumption. Many medical professionals believe that eating too much red meat increases the risk of heart disease and cancer. Suppose you would like to conduct a survey to determine the yearly consumption of beef by a typical American and want to use 1.35 kilograms as the desired margin of
27. Salaries of Business Graduates. Annual starting salaries for college graduates with degrees in business administration are generally expected to be between$45,000 and $60,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the
26. Gasoline Prices. The U.S. Energy Information Administration (US EIA) reported that the average price for a liter of regular gasoline is $0.78. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is$.07 for the price of a liter of regular
25. Computer-Assisted Training. Refer to the Scheer Industries example in Section 8.2.Use 6.84 days as a planning value for the population standard deviation.a. Assuming 95% confidence, what sample size would be required to obtain a margin of error of 1.5 days?b. If the precision statement was made
24. The range for a set of data is estimated to be 36.a. What is the planning value for the population standard deviation?b. At 95% confidence, how large a sample would provide a margin of error of 3?c. At 95% confidence, how large a sample would provide a margin of error of 2?
23. How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10? Assume that the population standard deviation is 40.
22. Movie Ticket Sales. Marvel Studio’s motion picture Guardians of the Galaxy opened over the first two days of the 2014 Labor Day weekend to a then recordbreaking$94.3 million in ticket sales revenue in North America. The ticket sales revenue in dollars for a sample of 30 theaters during the
21. Telemedicine. Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments(Bloomberg Businessweek, March 4–9, 2014).
20. Automobile Insurance Premiums. The average annual premium for automobile insurance in the United States is $1503. The following annual premiums ($) are representative of the website’s findings for the state of Michigan.1905 3112 2312 2725 2545 2981 2677 2525 2627 2600 2370 2857 2962 2545 2675
19. Meal Cost in Hong Kong. The mean cost of a meal for two in a midrange restaurant in Tokyo is $40 (Numbeo.com website). How do prices for comparable meals in Hong Kong compare? The file HongKongMeals contains the costs for a sample of 42 recent meals for two in Hong Kong midrange restaurants.a.
18. Unemployment in Older Workers. Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job contained in the file JobSearch are consistent with the AARP findings.a.
17. Quality Ratings of Airports. The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to
16. Years to Bond Maturity. A sample containing years to maturity and yield for 40 corporate bonds are contained in the file CorporateBonds.a. What is the sample mean years to maturity for corporate bonds and what is the sample standard deviation?b. Develop a 95% confidence interval for the
15. Weekly Sales Reports. Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2. Provide 90% and 95% confidence
14. A simple random sample with n = 54 provided a sample mean of 22.5 and a sample standard deviation of 4.4.a. Develop a 90% confidence interval for the population mean.b. Develop a 95% confidence interval for the population mean.c. Develop a 99% confidence interval for the population mean.d. What
13. The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5.a. What is the point estimate of the population mean?b. What is the point estimate of the population standard deviation?c. With 95% confidence, what is the margin of error for the estimation of the population
12. Find the t value(s) for each of the following cases.a. Upper tail area of .025 with 12 degrees of freedomb. Lower tail area of .05 with 50 degrees of freedomc. Upper tail area of .01 with 30 degrees of freedomd. Where 90% of the area falls between these two t values with 25 degrees of freedome.
11. For a t distribution with 16 degrees of freedom, find the area, or probability, in each region.a. To the right of 2.120b. To the left of 1.337c. To the left of −1.746d. To the right of 2.583e. Between −2.120 and 2.120f. Between −1.746 and 1.746
10. Assisted-Living Facility Rent. Costs are rising for all kinds of medical care. The mean monthly rent at assistedliving facilities was reported to have increased 17%over the last five years to $3486. Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can
9. Cost to Repair Fire Damage. The mean cost to repair the smoke and fire damage that results from home fires of all causes is $11,389 (HomeAdvisor). How does the damage that results from home fires caused by careless use of tobacco compare?The file TobaccoFires provides the cost to repair smoke
8. Cost of Message Therapy Sessions. Studies show that massage therapy has a variety of health benefits and it is not too expensive. A sample of 10 typical onehour massage therapy sessions showed an average charge of $59. The population standard deviation for a onehour session is s = $5.50.a. What
7. Cost of Dog Ownership. Money reports that the average annual cost of the first year of owning and caring for a large dog in 2017 is $1448. The Irish Red and White Setter Association of America has requested a study to estimate the annual firstyear cost for owners of this breed. A sample of 50
6. Travel Taxes. In an attempt to assess total daily travel taxes in various cities, the Global Business Travel Association conducted a study of daily travel taxes on lodging, rental car, and meals. The data contained in the file TravelTax are consistent with the findings of that study for business
5. Restaurant Bills. Data were collected on the amount spent by 64 customers for lunch at a major Houston restaurant. These data are contained in the file Houston. Based upon past studies the population standard deviation is known with s = $6.a. At 99% confidence, what is the margin of error?b.
4. A 95% confidence interval for a population mean was reported to be 152 to 160. If s = 15, what sample size was used in this study?
3. A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is s = 15.a. Compute the 95% confidence interval for the population mean.b. Assume that the same sample mean was obtained from a sample of 120 items.Provide a 95% confidence interval for the
2. A simple random sample of 50 items from a population with s = 6 resulted in a sample mean of 32.a. Provide a 90% confidence interval for the population mean.b. Provide a 95% confidence interval for the population mean.c. Provide a 99% confidence interval for the population mean.
1. A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is s = 5.a. What is the standard error of the mean, sx?b. At 95% confidence, what is the margin of error?
66. U.S. Drivers and Speeding. ABC News reports 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 random
65. Undeliverable Mail Pieces. Of the 155 billion mailpieces the U.S. Postal Service(USPS) processed and delivered in 2017, 4.3% were undeliverable as addressed. Suppose that a brief questionnaire about USPS service is attached to each mailpiece in a random sample of 114,250 mailpieces.a. What is
64. Typical Home Internet Usage. According to USC Annenberg, the mean time spent by Americans on the Internet in their home per week is 17.6 hours. Assume that the standard deviation for the time spent by Americans on the Internet in their home per week is 5.1 hours. Suppose the Florida Department
63. Life of Compact Fluorescent Lights. In 2018, the Simple Dollar website reported that the mean life of 14-watt compact fluorescent lights (CFLs) is 8000 hours. Assume that for this population the standard deviation for CFL life is 480. Suppose the U.S.Department of Energy would like to select a
62. Textbook Publishing. Lori Jeffrey is a successful sales representative for a major publisher of college textbooks. Historically, Lori obtains a book adoption on 25% of her sales calls. Viewing her sales calls for one month as a sample of all possible sales calls, assume that a statistical
61. Traffic Tickets. The proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one traffic ticket during a five-year period is .15.a. Show the sampling distribution of p if a random sample of 150 insured individuals is used to estimate the proportion
60. Internet Advertising. Advertisers contract with Internet service providers and search engines to place ads on websites. They pay a fee based on the number of potential customers who click on their ad. Unfortunately, click fraud—the practice of someone clicking on an ad solely for the purpose
59. Marketing Research Telephone Surveys. A market research firm conducts telephone surveys with a 40% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the
58. Australians and Smoking. Reuters reports that 15 percent of Australians smoke. By introducing tough laws banning brand labels on cigarette packages, Australia hopes to ultimately reduce the percentage of people smoking to 10%. Answer the following questions based on a sample of 240
57. Production Quality Control. A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights x. If test results over a long period of time show that 5% of the x values
56. Survey Research Results. A researcher reports survey results by stating that the standard error of the mean is 20. The population standard deviation is 500.a. How large was the sample used in this survey?b. What is the probability that the point estimate was within ±25 of the population mean?
55. Inventory Costs. Three firms carry inventories that differ in size. Firm A’s inventory contains 2000 items, firm B’s inventory contains 5000 items, and firm C’s inventory contains 10,000 items. The population standard deviation for the cost of the items in each firm’s inventory is s =
54. University Costs. After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175. Assume the population standard deviation is $7400. Suppose that a random sample of 60 USC students will be taken from this population.a. What is the value
53. Airline Fares. The mean airfare for flights departing from Buffalo Niagara International Airport during the first three months of 2017 was $320.51. Assume the standard deviation for this population of fares is known to be $80. Suppose a random sample of 60 flights departing from Buffalo Niagara
52. Foot Locker Store Productivity. Foot Locker uses sales per square meter as a measure of store productivity. Sales are currently running at an annual rate of $4060 per square meter. You have been asked by management to conduct a study of a sample of 64 Foot Locker stores. Assume the standard
51. Personal Health Expenditures. Data made available through the Petersen-Kaiser Health System Tracker in May 2018 showed health expenditures were $10,348 per person in the United States. Use $10,348 as the population mean and suppose a survey research firm will take a sample of 100 people to
50. Shadow Stocks. Jack Lawler, a financial analyst, wants to prepare an article on the Shadow Stock portfolio developed by the American Association of Individual Investors (AAII). A list of the 30 companies in the Shadow Stock portfolio is contained in the file ShadowStocks. Jack would like to
49. Landline Telephone Service. According to the U.S. Department of Health and Human Services, only 49.2% of homes in the United States used landline telephone service in 2017.a. Suppose a sample of 207,000 U.S. homes will be taken to learn about home telephone usage. Show the sampling distribution
48. Repeat Purchases. The president of Colossus.com, Inc., believes that 42% of the firm’s orders come from customers who have purchased from Colossus.com in the past. A random sample of 108,700 orders from the past six months will be used to estimate the proportion of orders placed by repeat
47. KMPL for New Cars. The New York Times reported that 17.2 million new cars and light trucks were sold in the United States in 2017, and the U.S. Environmental Protection Agency projects the average efficiency for these vehicles to be 10.7 kilometers per liter. Assume that the population standard
46. Vacation Hours Earned by Blue-Collar and Service Employees. The U.S. Bureau of Labor Statistics (BLS) reported that the mean annual number of hours of vacation time earned by blue-collar and service employees who work for small private establishments and have at least 10 years of service is
46. Vacation Hours Earned by Blue-Collar and Service Employees. The U.S. Bureau of Labor Statistics (BLS) reported that the mean annual number of hours of vacation time earned by blue-collar and service employees who work for small private establishments and have at least 10 years of service is
45. Assume that the population proportion is .44. Compute the standard error of the proportion, sp, for sample sizes of 500,000; 1,000,000; 5,000,000; 10,000,000; and 100,000,000. What can you say about the size of the standard error of the sample proportion as the sample size is increased?
44. A sample of size 100,000 is selected from a population with p 5 .75.a. What is the expected value of p?b. What is the standard error of p?c. Show the sampling distribution of p.d. What does the sampling distribution of p show?
43. Assume the population standard deviation is s 5 25. Compute the standard error of the mean, sx, for sample sizes of 500,000; 1,000,000; 5,000,000; 10,000,000; and 100,000,000. What can you say about the size of the standard error of the mean as the sample size is increased?
42. A population has a mean of 400 and a standard deviation of 100. A sample of size 100,000 will be taken, and the sample mean x will be used to estimate the population mean.a. What is the expected value of x?b. What is the standard deviation of x?c. Show the sampling distribution of x.d. What
41. Household Grocery Expenditures. The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population.a. Show the sampling distribution of p, the
40. Product Labeling. The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product’s label. Assume the population proportion is p = .76 and a sample of 400 consumers is selected from the population.a. Show the sampling distribution of the sample
39. Better Business Bureau Complaints. In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a
38. Unnecessary Medical Care. According to Reader’s Digest, 42% of primary care doctors think their patients receive unnecessary medical care.a. Suppose a sample of 300 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive
37. Food Waste. In 2017, the Restaurant Hospitality website reported that only 10%of surplus food is being recovered in the food-service and restaurant sector, leaving approximately 1.5 billion meals per year uneaten. Assume this is the true population proportion and that you plan to take a sample
36. Ages of Entrepreneurs. The Wall Street Journal reported that the age at first startup for 55% of entrepreneurs was 29 years of age or less and the age at first startup for 45% of entrepreneurs was 30 years of age or more.a. Suppose a sample of 200 entrepreneurs will be taken to learn about the
35. Orders from First-Time Customers. The president of Doerman Distributors, Inc., believes that 30% of the firm’s orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time customers.a. Assume that the president is correct and p =
34. The population proportion is .30. What is the probability that a sample proportion will be within ±.04 of the population proportion for each of the following sample sizes?a. n = 100b. n = 200c. n = 500d. n = 1000e. What is the advantage of a larger sample size?
33. Assume that the population proportion is .55. Compute the standard error of the proportion, sp, for sample sizes of 100, 200, 500, and 1000. What can you say about the size of the standard error of the proportion as the sample size is increased?
32. A population proportion is .40. A sample of size 200 will be taken and the sample proportion p will be used to estimate the population proportion.a. What is the probability that the sample proportion will be within ±.03 of the population proportion?b. What is the probability that the sample
31. A sample of size 100 is selected from a population with p = .40.a. What is the expected value of p?b. What is the standard error of p?c. Show the sampling distribution of p.d. What does the sampling distribution of p show?
30. Employee Ages. To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected.a. Would you use the finite population correction factor in calculating the standard error of the mean? Explain.b. If the population standard deviation is s = 8.2
29. Income Tax Return Preparation Fees. The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.a. What is the probability that the
28. State Rainfalls. The state of California has a mean annual rainfall of 56 centimeters, whereas the state of New York has a mean annual rainfall of 107 centimeters.Assume that the standard deviation for both states is 10 centimeters. A sample of 30 years of rainfall for California and a sample
27. College Graduate-Level Wages. The Economic Policy Institute periodically issues reports on worker’s wages. The institute reported that mean wages for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2017. Assume the standard deviation for
26. Federal Income Tax Returns. The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,642. Assume the standard
25. SAT Scores. In May 2018, The College Board reported the following mean scores for two parts of the Scholastic Aptitude Test (SAT):Evidence-Based Reading and Writing 533 Mathematics 527 Assume that the population standard deviation on each part of the test is s = 100.a. What is the probability a
24. U.S. Unemployment. Barron’s reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.5 weeks and that the population standard deviation is 4 weeks. Suppose
23. Finding Probabilities for Electronic Associates, Inc., Managers. In the EAI sampling problem (see Figure 7.5), we showed that for n = 30, there was .5034 probability of obtaining a sample mean within ±$500 of the population mean.a. What is the probability that x is within $500 of the
22. Sampling Distribution for Electronic Associates, Inc., Managers. Refer to the EAI sampling problem. Suppose a simple random sample of 60 managers is used.a. Sketch the sampling distribution of x when simple random samples of size 60 are used.b. What happens to the sampling distribution of x if
21. Suppose a random sample of size 50 is selected from a population with s = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).a. The population size is infinite.b. The population size is N = 50,000.c.
20. Assume the population standard deviation is s = 25. Compute the standard error of the mean, sx, for sample sizes of 50, 100, 150, and 200. What can you say about the size of the standard error of the mean as the sample size is increased?
19. A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimate m.a. What is the probability that the sample mean will be within ±5 of the population mean?b. What is the probability that the sample mean will be within ±10 of
18. A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the sample mean x will be used to estimate the population mean.a. What is the expected value of x?b. What is the standard deviation of x?c. Show the sampling distribution of x.d. What does the
17. Attitudes Toward Automation. The Pew American Trends Survey includes a series of questions on attitudes toward automation. The May 2018 results showed that 2977 of 4135 respondents are worried about a future in which robots and computers can do many human jobs, 2770 are worried about the
16. AARP Survey. In a sample of 426 U.S. adults age 50 and older, AARP asked how important a variety of issues were in choosing whom to vote for in the next presidential election.a. What is the sampled population for this study?b. Social Security and Medicare was cited as “very important” by
15. Rating Wines. According to Wine-Searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. Wine scores range from 0 to 100, with a score of 95–100 indicating a great wine, 90–94 indicating an outstanding wine, 85–89 indicating
14. Morningstar Stock Data. Morningstar publishes ratings data on 1208 company stocks. A sample of 40 of these stocks is contained in the file Morningstar. Use the Morningstar data set to answer the following questions.a. Develop a point estimate of the proportion of the stocks that receive
13. Monthly Sales Data. A sample of 5 months of sales data provided the following information:Month: 1 2 3 4 5 Units Sold: 94 100 85 94 92a. Develop a point estimate of the population mean number of units sold per month.b. Develop a point estimate of the population standard deviation.
12. A survey question for a sample of 150 individuals yielded 75 Yes responses, 55 No responses, and 20 No Opinions.a. What is the point estimate of the proportion in the population who respond Yes?b. What is the point estimate of the proportion in the population who respond No?12. A survey
11. The following data are from a simple random sample.5 8 10 7 10 14a. What is the point estimate of the population mean?b. What is the point estimate of the population standard deviation?
10. Sampling from Infinite Populations. Indicate which of the following situations involve sampling from a finite population and which involve sampling from an infinite population. In cases where the sampled population is finite, describe how you would construct a frame.a. Obtain a sample of
9. Returns on Mutual Finds. The Wall Street Journal provides the net asset value, the year-to-date percent return, and the three-year percent return for 882 mutual funds at the end of 2017. Assume that a simple random sample of 12 of the 882 mutual funds will be selected for a follow-up study on
8. DJIA Stocks. The following stocks make up the Dow Jones Industrial Average.1. 3M 11. Exxon Mobil 21. Microsoft 2. American Express 12. General Electric 22. Nike 3. Apple 13. Goldman Sachs 23. Pfizer 4. Boeing 14. Home Depot 24. Procter & Gamble 5. Caterpillar 15. IBM 25. Travelers Companies,
7. Sampling Doctors. Assume that we want to identify a simple random sample of 12 of the 372 doctors practicing in a particular city. The doctors’ names are available from a local medical organi zation. Use the eighth column of five-digit random numbers in Table 7.1 to identify the 12 doctors for
6. Census Bureau County Data. The County and City Data Book, published by the Census Bureau, lists information on 3139 counties throughout the United States.Assume that a national study will collect data from 30 randomly selected counties. Use four-digit random numbers from the last column of Table
5. Pass–Fail Grading. A student government organization is interested in estimating the proportion of students who favor a mandatory “pass-fail” grading policy for elective courses. A list of names and addresses of the 645 students enrolled during the current quarter is available from the
4. Investigating Trading Practices. The 10 most active stocks on the New York Stock Exchange for a given week, are shown here.AT&T Alcatel Lucent Exxon Mobile Petrobras Vale SA Pfizer Verizon Gen. Elect. Citigroup Ford Exchange authorities decided to investigate trading practices using a sample of
3. Industrial Stock Performance. Fortune publishes data on sales, profits, assets, stockholders’equity, market value, and earnings per share for the 500 largest U.S. industrial corporations every year. Assume that you want to select a simple random sample of 10 corporations from the Fortune 500
2. Assume a finite population has 350 elements. Using the last three digits of each of the following five-digit random numbers (e.g., 601, 022, 448, . . . ), determine the first four elements that will be selected for the simple random sample.98601 73022 83448 02147 34229 27553 84147 93289 14209
1. Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples of size 2 can be selected.a. List the 10 samples beginning with AB, AC, and so on.b. Using simple random sampling, what is the probability that each sample of size 2 is selected?c.
54. Calls to Insurance Claims Office. The time (in minutes) between telephone calls at an insurance claims office has the following exponential probability distribution.f (x) 5 .50e2.50x for x $ 0a. What is the mean time between telephone calls?b. What is the probability of having 30 seconds or
53. Waiting in Line at Kroger. Do you dislike waiting in line? Supermarket chain Kroger has used computer simulation and information technology to reduce the average waiting time for customers at 2300 stores. Using a new system called Que-Vision, which allows Kroger to better predict when shoppers
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