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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
22. Carolina Industries Product Demand. The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand.Unit Demand Probability 300 .20 400 .30 500 .35
21. IS Managers Job Satisfaction. The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).Job Satisfaction Score IS Senior Executives
20. Automobile Insurance Damage Claims. The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.Payment ($) Probability 0 .85 500 .04 1000 .04 3000 .03 5000 .02 8000 .01 10000 .01a. Use the expected collision payment to determine
19. New Tax Accounting Clients. New legislation passed in 2017 by the U.S. Congress changed tax laws that affect how many people file their taxes in 2018 and beyond.These tax law changes will likely lead many people to seek tax advice from their accountants (The New York Times). Backen and Hayes
18. Water Supply Stoppages. The following data has been collected on the number of times that owneroccupied and renteroccupied units had a water supply stoppage lasting 6 or more hours in the past 3 months.Number of Units (1000s)Number of Times Owner Occupied Renter Occupied 0 439 394 1 1100 760 2
17. Golf Scores. During the summer of 2018, Coldstream Country Club in Cincinnati, Ohio, collected data on 443 rounds of golf played from its white tees. The data for each golfer’s score on the twelfth hole are contained in the DATAfile Coldstream12.a. Construct an empirical discrete probability
16. The following table provides a probability distribution for the random variable y.y f (y)2 .20 4 .30 7 .40 8 .10a. Compute E( y).b. Compute Var( y) and s.
15. The following table provides a probability distribution for the random variable x.x f(x)3 .25 6 .50 9 .25a. Compute E(x), the expected value of x.b. Compute s2, the variance of x.c. Compute s, the standard deviation of x.
14. MRA Company Projected Profits. The following table is a partial probability distribution for the MRA Company’s projected profits (x = profit in $1000s) for the first year of operation (the negative value denotes a loss).x f(x)−100 .10 0 .20 50 .30 100 .25 150 .10 200a. What is the proper
13. Establishing Patient Trust. A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient’s trust. The following probability function has been
12. New Cable Subscribers. Spectrum provides cable television and Internet service to millions of customers. Suppose that the management of Spectrum subjectively assesses a probability distribution for the number of new subscribers next year in the state of New York as follows.x f(x)100,000 .10
11. Mailing Machine Malfunctions. A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency.a. Develop a probability distribution
10. Job Satisfaction of IS Managers. The percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers are as follows. The scores range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).Job Satisfaction
9. Employee Retention. Employee retention is a major concern for many companies. A survey of Americans asked how long they have worked for their current employer (Bureau of Labor Statistics website). Consider the following example of sample data of 2000 college graduates who graduated five years
8. Operating Room Use. The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20day period: On three of the days only one operating room was used, on five of the days two were used, on eight of the days three were used, and on four days
7. The probability distribution for the random variable x follows.x f(x)20 .20 25 .15 30 .25 35 .40a. Is this probability distribution valid? Explain.b. What is the probability that x = 30?c. What is the probability that x is less than or equal to 25?d. What is the probability that x is greater
6. Types of Random Variables. Listed below is a series of experiments and associated random variables. In each case, identify the values that the random variable can assume and state whether the random variable is discrete or continuous.Experiment Random Variable (x)a. Take a 20-question
5. Blood Test Analysis. To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps.a. List the experimental outcomes associated with
4. Unemployment in Northeastern States. The Census Bureau includes nine states in what it defines as the Northeast region of the United States. Assume that the government is interested in tracking unemployment in these nine states and that the random variable of interest is the number of
3. Interviews at Brookwood Institute. Three students scheduled interviews for summer employment at the Brookwood Institute. In each case the interview results in either an offer for a position or no offer. Experimental outcomes are defined in terms of the results of the three interviews.a. List the
2. Consider the experiment of a worker assembling a product.a. Define a random variable that represents the time in minutes required to assemble the product.b. What values may the random variable assume?c. Is the random variable discrete or continuous?
1. Consider the experiment of tossing a coin twice.a. List the experimental outcomes.b. Define a random variable that represents the number of heads occurring on the two tosses.c. Show what value the random variable would assume for each of the experimental outcomes.d. Is this random variable
45. Americans Without Health Insurance. The National Center for Health Statistics, housed within the U.S. Centers for Disease Control and Prevention (CDC), tracks the number of adults in the United States who have health insurance. According to this agency, the uninsured rates for Americans in 2018
44. Golf Equipment Website Visitors. ParFore created a website to market golf equipment and golf apparel. Management would like a special pop-up offer to appear for female website visitors and a different special pop-up offer to appear for male website visitors. From a sample of past website
43. Prostate Cancer Screening. According to a 2018 article in Esquire magazine, approximately 70% of males over age 70 will develop cancerous cells in their prostate.Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States. One of the most
42. Credit Card Defaults. A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 5% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of
41. Consulting Firm Bids. A consulting firm submitted a bid for a large research project.The firm’s management initially felt they had a 50–50 chance of getting the project.However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past
40. The prior probabilities for events A1, A2, and A3 are P(A1) = .20, P(A2) = .50, and P(A3) = .30. The conditional probabilities of event B given A1, A2, and A3 are P(B ∣ A1) = .50, P(B ∣ A2) = .40, and P(B ∣ A3) = .30.a. Compute P(B ∩ A1), P(B ∩ A2), and P(B ∩ A3).b. Apply Bayes’
39. The prior probabilities for events A1 and A2 are P(A1) = .40 and P(A2) = .60. It is also known that P(A1 ∩ A2) = 0. Suppose P(B ∣ A1) = .20 and P(B ∣ A2) = .05.a. Are A1 and A2 mutually exclusive? Explain.b. Compute P(A1 ∩ B) and P(A2 ∩ B).c. Compute P(B).d. Apply Bayes’ theorem to
38. Payback of Student Loans. The Institute for Higher Education Policy, a Washington, D.C.-based research firm, studied the payback of student loans for 1.8 million college students who had student loans that began to become due six years ago (The Wall Street Journal). The study found that 50% of
37. Giving Up Electronics. A 2018 Pew Research Center survey found that more Americans believe they could give up their televisions than could give up their cell phones(Pew Research website). Assume that the following table represents the joint probabilities of Americans who could give up their
36. NBA Free Throws. Suppose that a particular NBA player makes 93% of his free throws. Assume that late in a basketball game, this player is fouled and is awarded two shots.a. What is the probability that he will make both shots?b. What is the probability that he will make at least one shot?c.
35. Better at Getting Deals. To better understand how husbands and wives feel about their finances, Money magazine conducted a national poll of 1010 married adults age 25 and older with household incomes of $50,000 or more (Money website).Consider the following example set of responses to the
34. On-Time Performance of Airlines. The Bureau of Transportation Statistics reports on-time performance for airlines at major U.S. airports. JetBlue, United, and US Airways share terminal C at Boston’s Logan Airport. Suppose that the percentage of on-time flights reported was 76.8% for JetBlue,
33. Intent to Pursue MBA. Students taking the Graduate Management Admissions Test(GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows.Undergraduate Major Business Engineering Other Totals Intended
32. Living with Family. Consider the following example survey results of 18- to 34-yearolds in the United States, in response to the question “Are you currently living with your family?”Yes No Totals Men Women 106 92 141 161 247 253 Totals 198 302 500a. Develop the joint probability table for
31. Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = .30 and P(B) = .40.a. What is P(A ∩ B)?b. What is P(A ∣ B)?c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same,
30. Suppose that we have two events, A and B, with P(A) = .50, P(B) = .60, and P(A ∩ B) = .40.a. Find P(A ∣ B).b. Find P(B ∣ A).c. Are A and B independent? Why or why not?
29. Ivy League Admissions. High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants.Suppose that for a recent admissions class, an
28. Survey on Car Rentals. A survey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons.a. What
27. Social Media Use. A marketing firm would like to test-market the name of a new energy drink targeted at 18- to 29-year-olds via social media. A study by the Pew Research Center found that 35% of U.S. adults (18 and older) do not use social media (Pew Research Center website, October 2015). The
26. Morningstar Mutual Fund Ratings. Information about mutual funds provided by Morningstar includes the type of mutual fund ( Domestic Equity, International Equity, or Fixed Income) and the Morningstar rating for the fund. The rating is expressed from 1-star ( lowest rating) to 5-star ( highest
25. Americans Using Facebook and LinkedIn. A 2018 Pew Research Center survey(Pew Research website) examined the use of social media platforms in the United States. The survey found that there is a .68 probability that a randomly selected American will use Facebook and a .25 probability that a
24. Clarkson University Alumni Survey. Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The
23. Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, . . . , E7 denote the sample points. The following probability assignments apply: P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05. Let A 5 B 5 C 5{E1, E4, E6}{E2,
22. Suppose that we have a sample space with five equally likely experimental outcomes:E1, E2, E3, E4, E5. Let A 5 B 5 C 5{E1, E2}{E3, E4}{E2, E3, E5}a. Find P(A), P(B), and P(C).b. Find P(A • B). Are A and B mutually exclusive?c. Find Ac, Cc, P(Ac), and P(Cc).d. Find A • Bc and P(A • Bc).e.
21. Fatal Collisions with a Fixed Object. The National Highway Traffic Safety Administration (NHTSA) collects traffic safety-related data for the U.S. Department of Transportation. According to NHTSA’s data, 10,426 fatal collisions in 2016 were the result of collisions with fixed objects (NHTSA
20. Age of Financial Independence. Suppose that the following table represents a sample of 944 teenagers’ responses to the question, “When do you think you will become financially independent?”Age of Financially Independent Number of Responses 16 to 20 191 21 to 24 467 25 to 27 244 28 or
19. Impact of Global Warming. Do you think global warming will have an impact on you during your lifetime? A 2014 CBS News/New York Times poll of 1000 adults in the United States asked this question (CBS News website). Consider the responses by age groups shown below.Response Age 18229 301 Yes 134
18. Corporate Headquarters Locations. Each year Fortune magazine publishes an annual list of the 500 largest companies in the United States. The corporate headquarters for the 500 companies are located in 38 different states. The following table shows the 8 states with the largest number of Fortune
17. KP&L Project Over Budget. Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3.a. The design stage (stage 1) will run over budget if it takes 4 months to complete.List the sample points in the event the design stage is over budget.b. What is the probability that
16. Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice.a. How many sample points are possible? (Hint: Use the counting rule for multiple-step experiments.)b. List the sample points.c. What is the probability of
15. Consider the experiment of selecting a playing card from a deck of 52 playing cards.Each card corresponds to a sample point with a 1/52 probability.a. List the sample points in the event an ace is selected.b. List the sample points in the event a club is selected.c. List the sample points in
14. An experiment has four equally likely outcomes: E1, E2, E3, and E4.a. What is the probability that E2 occurs?b. What is the probability that any two of the outcomes occur (e.g., E1 or E3)?c. What is the probability that any three of the outcomes occur (e.g., E1 or E2 or E4)?
13. Powerball Lottery. The Powerball lottery is played twice each week in 44 states, the District of Columbia, and the Virgin Islands. To play Powerball, a participant must purchase a $2 ticket, select five numbers from the digits 1 through 69, and then select a Powerball number from the digits 1
12. Toothpaste Package Designs. A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual
11. Tri-State Smokers. A Gallup Poll of U.S. adults indicated that Kentucky is the state with the highest percentage of smokers (Gallup website). Consider the following example data from the Tri-State region, an area that comprises northern Kentucky, southeastern Indiana, and southwestern
10. Code Churn. Code Churn is a common metric used to measure the efficiency and productivity of software engineers and computer programmers. It’s usually measured as the percentage of a programmer’s code that must be edited over a short period of time. Programmers with higher rates of code
9. Sampling Bank Accounts. Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts
8. Zoning Changes. In the city of Milford, applications for zoning changes go through a two-step process: a review by the planning commission and a final decision by the city council. At step 1 the planning commission reviews the zoning change request and makes a positive or negative recommendation
7. A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E1) = .10, P(E2) = .15, P(E3) = .40, and P(E4) = .20. Are these prob a bility assignments valid? Explain.
6. An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 occurred 13 times, and E3 occurred 17 times. Assign probabilities to the outcomes. What method did you use?
5. Suppose an experiment has five equally likely outcomes: E1, E2, E3, E4, E5. Assign prob abilities to each outcome and show that the requirements in equations (4.3) and(4.4) are satisfied. What method did you use?
4. Consider the experiment of tossing a coin three times.a. Develop a tree diagram for the experiment.b. List the experimental outcomes.c. What is the probability for each experimental outcome?
3. How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.
2. How many ways can three items be selected from a group of six items? Use the letters A, B, C, D, E, and F to identify the items, and list each of the different combinations of three items.
1. An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?
75. Annual Returns for Panama Railroad Company Stock. The Panama Railroad Company was established in 1850 to construct a railroad across the isthmus that would allow fast and easy access between the Atlantic and Pacific Oceans. The following table provides annual returns for Panama Railroad stock
74. Automobile Speeds. Automobiles traveling on a road with a posted speed limit of 90 kilometers per hour are checked for speed by a state police radar system. Following is a frequency distribution of speeds.Speed(kilometers per hour) Frequency 76–82 10 83–89 40 90–96 150 97–103 175
73. Money Market Funds Days to Maturity. The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided. Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market
72. MLB Team Winning Percentages. Does a major league baseball team’s record during spring training indicate how the team will play during the regular season?Over a six-year period, the correlation coefficient between a team’s winning percentage in spring training and its winning percentage in
71. NFL Teams Worth. In 2014, the 32 teams in the National Football League (NFL)were worth, on average, $1.17 billion, 5% more than in 2013. The following data show the annual revenue ($ millions) and the estimated team value ($ millions) for the 32 NFL teams in 2014 (Forbes website).Team Revenue
70. Best Hotels. Travel + Leisure magazine provides an annual list of the 500 best hotels in the world. The magazine provides a rating for each hotel along with a brief description that includes the size of the hotel, amenities, and the cost per night for a double room. A sample of 12 of the
69. Restaurant Chains’ Sales per Store. The data contained in the file FoodIndustry show the company/chain name, the average sales per store ($1000s), and the food segment industry for 47 restaurant chains (Quick Service Restaurant Magazine website).a. What was the mean U.S. sales per store for
68. Household Incomes. The following data represent a sample of 14 household incomes($1000s). Answer the following questions based on this sample.49.4 52.4 53.4 51.3 52.1 48.7 52.1 52.2 64.5 51.6 46.5 52.9 52.5 51.2a. What is the median household income for these sample data?b. According to a
67. Work Commuting Methods. Public transportation and the automobile are two methods an employee can use to get to work each day. Samples of times recorded for each method are shown. Times are in minutes.Public Transportation: 28 29 32 37 33 25 29 32 41 34 Automobile: 29 31 33 32 34 30 31 32 35
66. Smartphone Use. Smartphones have become ubiquitous for most people and have become the predominant means of communication among people. Consider the following data indicating the number of minutes in a month spent interacting with others via a smartphone for a sample of 50 smartphone users.353
65. Worker Productivity and Insomnia. U.S. companies lose $63.2 billion per year from workers with insomnia. Accordign to a 2013 article in the Wall Street Journal, workers lose an average of 7.8 days of productivity per year due to lack of sleep. The following data show the number of hours of
64. Physician Office Waiting Times. The average waiting time for a patient at an El Paso physician’s office is just over 29 minutes, well above the national average of 21 minutes. In order to address the issue of long patient wait times, some physician’s offices are using wait tracking systems
63. NCAA Football Coaches Salaries. A 2017 USA Today article reports that NCAA football coaches’ salaries have continued to increase in recent years (USA Today). The annual base salaries for the previous head football coach and the new head football coach at 23 schools are given in the file
62. Americans Dining Out. Americans tend to dine out multiple times per week. The number of times a sample of 20 families dined out last week provides the following data.6 1 5 3 7 3 0 3 1 3 4 1 2 4 1 0 5 6 3 1a. Compute the mean and median.b. Compute the first and third quartiles.c. Compute the
61. Best Private Colleges. A random sample of 30 colleges from Kiplinger’s list of the best values in private college provided the data shown in the file BestPrivateColleges(Kiplinger website). The variable named Admit Rate (%) shows the percentage of students that applied to the college and were
60. Stock Market Indexes Comparison. The Russell 1000 is a stock market index consisting of the largest U.S. companies. The Dow Jones Industrial Average is based on 30 large companies. The file Russell gives the annual percentage returns for each of these stock indexes for the years 1988 to 2012
59. Smoke Detector Use and Death Rates. Over the past 40 years, the percentage of homes in the United States with smoke detectors has risen steadily and has plateaued at about 96% as of 2015 (National Fire Protection Association website).With this increase in the use of home smoke detectors, what
58. Driving Speed and Fuel Efficiency. A department of transportation’s study on driving speed and kilometers per liter for midsize automobiles resulted in the following data:Speed (Kilometers per Hour) 50 80 65 90 50 40 95 40 80 90 Kilometers per Liter 11.8 10.6 10.6 9.7 12.7 13.5 8.9 14.8 11.0
57. Stock Price Comparison. The file StockComparison contains monthly adjusted stock prices for technology company Apple, Inc., and consumer-goods company Procter & Gamble(P&G) from 2013–2018.a. Develop a scatter diagram with Apple stock price on the horizontal axis and P&G stock price on the
56. Five observations taken for two variables follow.xi 6 11 15 21 27 yi 6 9 6 17 12a. Develop a scatter diagram for these data.b. What does the scatter diagram indicate about a relationship between x and y?c. Compute and interpret the sample covariance.d. Compute and interpret the sample
55. Five observations taken for two variables follow.xi 4 6 11 3 16 yi 50 50 40 60 30a. Develop a scatter diagram with x on the horizontal axis.b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?c. Compute and interpret the sample
54. U.S. Border Crossings. The Bureau of Transportation Statistics keeps track of all border crossings through ports of entry along the U.S.-Canadian and U.S.-Mexican borders. The data contained in the file BorderCrossings show the most recently published figures for the number of personal vehicle
53. Most Admired Companies. Fortune magazine’s list of the world’s most admired companies for 2014 is provided in the data contained in the file AdmiredCompanies(Fortune magazine website). The data in the column labeled “Return” shows the one-year total return (%) for the top ranked 50
52. Cell Phone Companies Customer Satisfaction. Consumer Reports provides overall customer satisfaction scores for AT&T, Sprint, T-Mobile, and Verizon cell-phone services in major metropolitan areas throughout the United States. The rating for each service reflects the overall customer satisfaction
51. Pharmaceutical Company Sales. Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.8408 1374 1872 8879 2459 11413 608 14138 6452 1850 2818 1356 10498 7478 4019 4341 739 2127 PharmacySales 3653 5794 8305a. Provide a five-number summary.b. Compute the lower and upper
50. Naples Half-Marathon Times. Naples, Florida, hosts a half-marathon (13.1-mile race) in January each year. The event attracts top runners from throughout the United States as well as from around the world. In the race results shown below 22 men and 31 women entered the 19–24 age class. Finish
49. A data set has a first quartile of 42 and a third quartile of 50. Compute the lower and upper limits for the corresponding boxplot. Should a data value of 65 be considered an outlier?
48. Show the five-number summary and the boxplot for the following data: 5, 15, 18, 10, 8, 12, 16, 10, 6.
47. Show the boxplot for the data in exercise 46.
46. Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Provide the five-number summary for the data.
45. Apple iPads in Schools. The New York Times reported that Apple has unveiled a new iPad marketed specifically to school districts for use by students (The New York Times website). The 24.6-centimeter iPads will have faster processors and a cheaper price point in an effort to take market share
44. NCAA Basketball Game Scores. A sample of 10 NCAA college basketball game scores provided the following data.Winning Team Points Losing Team Points Winning Margin Arizona Duke Florida State Kansas Kentucky Louisville Oklahoma State Purdue Stanford Wisconsin 90 85 75 78 71 65 72 76 77 76 Oregon
43. Best Places to Live. Each year Money magazine publishes a list of “Best Places to Live in the United States.” These listings are based on affordability, educational performance, convenience, safety, and livability. The list below shows the median household income of Money magazine’s top
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