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The Practice Of Statistics For Business And Economics 4th Edition Layth C. Alwan, Bruce A. Craig - Solutions

Draw a tree diagram. Refer to the previous exercise. Draw a tree diagram to illustrate the probabilities in a situation in which you first identify the type of institution attended and then identify the gender of the student.
Attendance at two-year and four-year colleges. In a large national population of college students, 61% attend four-year institutions and the rest attend two-year institutions. Males make up 44% of the students in the four-year institutions and 41% of the students in the two-year institutions.(a)
What’s wrong? In each of the following scenarios, there is something wrong. Describe what is wrong and give a reason for your answer.(a) P(A or B) is always equal to the sum of P(A)and P(B).(b) The probability of an event minus the probability of its complement is always equal to 1.(c) Two events
Find the probabilities. Suppose that the probability that A occurs is 0.6 and the probability that A and B occur is 0.5.(a) Find the probability that B occurs given that A occurs.(b) Illustrate your calculations in part (a) using a Venn diagram.
Conditional probabilities. Suppose that P(A) 5 0.5, P(B) 5 0.3, and P(B u A) 5 0.2.(a) Find the probability that both A and B occur.(b) Use a Venn diagram to explain your calculation.(c) What is the probability of the event that B occurs and A does not?
Unions.(a) Assume that P(A) 5 0.4, P(B) 5 0.3, and P(C) 5 0.1.If the events A, B, and C are disjoint, find the probability that the union of these events occurs.(b) Draw a Venn diagram to illustrate your answer to part (a).(c) Find the probability of the complement of the union of A, B, and C.
Find and explain some probabilities.(a) Can we have an event A that has negative probability?Explain your answer.(b) Suppose P(A) 5 0.2 and P(B) 5 0.4. Explain what it means for A and B to be disjoint. Assuming that they are disjoint, find the probability that A or B occurs.(c) Explain in your own
Labor rates. Refer to the labor data in Example 4.18 (page 197). Draw a tree diagram with the first-stage branches being gender. Then, off the gender branches, draw two branches as the outcomes being “labor force participating’’versus “not in the labor force.’’ Show how the tree would
Find the conditional probability. Refer to Example 4.20. What is the probability that a student is part-time, given that the student is 15 to 19 years old? Explain in your own words the difference between this calculation and the one that we did in Example 4.20.
What rule did we use? In Example 4.20, we calculated P(A). What rule did we use for this calculation? Explain why this rule applies in this setting.
Buying from Japan. Functional Robotics Corporation buys electrical controllers from a Japanese supplier. The company’s treasurer thinks that there is probability 0.4 that the dollar will fall in value against the Japanese yen in the next month. The treasurer also believes that if the dollar
Focus group probabilities. A focus group of 15 consumers has been selected to view a new TV commercial. Even though all of the participants will provide their opinion, two members of the focus group will be randomly selected and asked to answer even more detailed questions about the commercial. The
Men labor participating. Refer to Example 4.18. What is the probability that a person is labor participant given the person is male?
Probability that sum of dice is even or greater than 8. Suppose you roll a pair of dice and record the sum of the dice. What is the probability that the sum is even or greater than 8?
Probability that sum of dice is a multiple of 4. Suppose you roll a pair of dice and you record the sum of the dice. What is the probability that the sum is a multiple of 4?If events A and B are not disjoint, they can occur simultaneously. The probability of their union is then less than the sum of
Independence of complements. Show that if events A and B obey the multiplication rule, P(A and B) 5 P(A)P(B), then A and the complement Bc of B also obey the multiplication rule, P(A and Bc) 5 P(A)P(Bc). That is, if events A and B are independent, then A and Bc are also independent. (Hint: Start by
Axioms of probability. Show that any assignment of probabilities to events that obeys Rules 2 and 3 on page 182 automatically obeys the complement rule (Rule 4). This implies that a mathematical treatment of probability can start from just Rules 1, 2, and 3. These rules are sometimes called axioms
Playing the lottery. An instant lottery game gives you probability 0.02 of winning on any one play. Plays are independent of each other. If you play five times, what is the probability that you win at least once?
What’s wrong? In each of the following scenarios, there is something wrong. Describe what is wrong and give a reason for your answer.(a) If the sample space consists of two outcomes, then each outcome has probability 0.5.(b) If we select a digit at random, then the probability of selecting a 2 is
What’s wrong? In each of the following scenarios, there is something wrong. Describe what is wrong and give a reason for your answer.(a) If two events are disjoint, we can multiply their probabilities to determine the probability that they will both occur.(b) If the probability of A is 0.6 and
The multiplication rule for independent events. The probability that a randomly selected person prefers the vehicle color white is 0.24. Can you apply the multiplication rule for independent events in the situations described in parts (a) and (b)? If your answer is Yes, apply the rule.(a) Two
A random walk on Wall Street? The “random walk’’ theory of securities prices holds that price movements in disjoint time periods are independent of each other. Suppose that we record only whether the price is up or down each year and that the probability that our portfolio rises in price in
Hiring strategy. A chief executive officer (CEO)has resources to hire one vice president or three managers.He believes that he has probability 0.6 of successfully recruiting the vice president candidate and probability 0.8 of successfully recruiting each of the manager candidates. The three
Everyone gets audited. Wallen Accounting Services specializes in tax preparation for individual tax returns. Data collected from past records reveals that 9% of the returns prepared by Wallen have been selected for audit by the Internal Revenue Service.Today, Wallen has six new customers. Assume
Using Internet sources. Internet sites often vanish or move, so references to them can’t be followed. In fact, 13% of Internet sites referenced in major scientific journals are lost within two years after publication.(a) If a paper contains seven Internet references, what is the probability that
Equally likely events. For each of the following situations, explain why you think that the events are equally likely or not.(a) The outcome of the next tennis match for Victoria Azarenka is either a win or a loss. (You might want to check the Internet for information about this tennis player.)(b)
Who goes to Paris? Abby, Deborah, Sam, Tonya, and Roberto work in a firm’s public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness, the choice will be made by drawing two names from a hat.(This is an SRS of size 2.)(a) Write down all
Legitimate probabilities? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate—that is, satisfies the rules of probability.If not, give specific reasons for your answer.(a) When a coin is spun, P(H) 5 0.55 and P(T) 5
Almond M&M’S. Exercise 4.39 gives the probabilities that an M&M candy is each of blue, orange, green, brown, yellow, and red. If “Almond’’M&M’S are equally likely to be any of these colors, what is the probability of drawing a blue Almond M&M?
Colors of M&M’S. The colors of candies such as M&M’S are carefully chosen to match consumer preferences. The color of an M&M drawn at random from a bag has a probability distribution determined by the proportions of colors among all M&M’S of that type.(a) Here is the distribution for plain
Stock market movements. You watch the price of the Dow Jones Industrial Index for four days.Give a sample space for each of the following random phenomena.(a) You record the sequence of up-days and down-days.(b) You record the number of up-days.
Land in Iowa. Choose an acre of land in Iowa at random. The probability is 0.92 that it is farmland and 0.01 that it is forest.(a) What is the probability that the acre chosen is not farmland?(b) What is the probability that it is either farmland or forest?(c) What is the probability that a
Car colors. Choose a new car or light truck at random and note its color. Here are the probabilities of the most popular colors for cars purchased in South America in 2012:14 Color Silver White Black Gray Red Brown Probability 0.29 0.21 0.19 0.13 0.09 0.05(a) What is the probability that a randomly
Modes of transportation. Governments (local and national) find it important to gather data on modes of transportation for commercial and workplace movement.Such information is useful for policymaking as it pertains to infrastructure (like roads and railways), urban development, energy use, and
World Internet usage. Approximately 40.4%of the world’s population uses the Internet (as of July 2014).12 Furthermore, a randomly chosen Internet user has the following probabilities of being from the given country of the world:Region China U.S. India Japan Probability 0.2197 0.0958 0.0833
Online health information. Based on a random sample of 1066 adults (18 years or older), a Harris Poll (July 13–18, 2010) estimates that 175 million U.S. adults have gone online for health information.Such individuals have been labeled as “cyberchondriacs.’’Cyberchondriacs in the sample were
Demographics—language. Canada has two official languages, English and French. Choose a Canadian at random and ask, “What is your mother tongue?’’ Here is the distribution of responses, combining many separate languages from the broad Asian/Pacific region:10 Language English French
Confidence in institutions. A Gallup Poll (June 1–4, 2013) interviewed a random sample of 1529 adults (18 years or older). The people in the sample were asked about their level of confidence in a variety of institutions in the United States. Here are the results for small and big businesses:9
Support for casino in Toronto. In an effort to seek the public’s input on the establishment of a casino, Toronto’s city council enlisted an independent analytics research company to conduct a public survey.A random sample of 902 adult Toronto residents were asked if they support the casino in
Bright lights? A string of holiday lights contains 20 lights. The lights are wired in series, so that if any light fails the whole string will go dark. Each light has probability 0.02 of failing during a three-year period. The lights fail independently of each other. What is the probability that
Failing to detect drug use. In Example 4.15, we considered how drug tests can indicate illegal drug use when no illegal drugs were actually used. Consider now another type of false test result. Suppose an employee is suspected of having used an illegal drug and is given two tests that operate
Misleading résumés. For more than two decades, Jude Werra, president of an executive recruiting firm, has tracked executive résumés to determine the rate of misrepresenting education credentials and/or employment information. On a biannual basis, Werra reports a now nationally recognized
College-educated part-time workers? For people aged 25 years or older, government data show that 34% of employed people have at least four years of college and that 20% of employed people work part-time. Can you conclude that because (0.34)(0.20) 5 0.068, about 6.8% of employed people aged 25 years
High school rank. Select a first-year college student at random and ask what his or her academic rank was in high school. Here are the probabilities, based on proportions from a large sample survey of first-year students:Rank Top 20% Second 20% Third 20% Fourth 20% Lowest 20%Probability 0.41 0.23
Possible outcomes for rolling a die. A die has six sides with one to six spots on the sides. Give the probability distribution for the six possible outcomes that can result when a fair die is rolled.
Use the addition rule. Use the addition rule (page 182) with the probabilities for the events A and B from Example 4.11 to find the probability of A or B.
Benford’s law. Using the probabilities for Benford’s law, find the probability that a first digit is anything other than 4.
Grading Canadian health care. Annually, the Canadian Medical Association uses the marketing research firm Ipsos Canada to measure public opinion with respect to the Canadian health care system. Between July 17 and July 26 of 2013, Ipsos Canada interviewed a random sample of 1000 adults.3 The people
Occupational deaths. Government data on job-related deaths assign a single occupation for each such death that occurs in the United States. The data on occupational deaths in 2012 show that the probability is 0.183 that a randomly chosen death was a construction worker and 0.039 that it was miner.
Moving up. An economist studying economic class mobility finds that the probability that the son of a father in the lowest economic class remains in that class is 0.46. What is the probability that the son moves to one of the higher classes?
White, black, silver, gray, or red. Refer to Example 4.8, and find the probability that the favorite color is white, black, silver, gray, or red using Rule 4.Explain why this calculation is easier than finding the answer using Rule 3.
Red or brown. Refer to Example 4.8, and find the probability that the favorite color is red or brown.
Describing sample spaces. In each of the following situations, describe a sample space S for the random phenomenon. Explain why, theoretically, a list of all possible outcomes is not finite.(a) You record the number of tosses of a die until you observe a six.(b) You record the number of tweets per
Describing sample spaces. In each of the following situations, describe a sample space S for the random phenomenon. In some cases, you have some freedom in your choice of S.(a) A new business is started. After two years, it is either still in business or it has closed.(b) A student enrolls in a
Thinking about probability statements. Probability is a measure of how likely an event is to occur. Match one of the probabilities that follow with each statement of likelihood given. (The probability is usually a more exact measure of likelihood than is the verbal statement.)0 0.01 0.3 0.6 0.99
Proportions of McDonald’s price changes.Continue the study of daily price changes of McDonald’s stock from the Exercise 4.9.Consider three possible outcomes: (1) positive price change, (2) no price change, and (3) negative price change. MCD(a) Find the proportions of each of these outcomes.
A question about dice. Here is a question that a French gambler asked the mathematicians Fermat and Pascal at the very beginning of probability theory: what is the probability of getting at least one 6 in rolling four dice? The Law of Large Numbers applet allows you to roll several dice and watch
Use the Probability applet. The idea of probability is that the proportion of heads in many tosses of a balanced coin eventually gets close to 0.5. But does the actual count of heads get close to one-half the number of tosses? Let’s find out. Set the“Probability of Heads’’ in the
Are McDonald’s price changes independent?Refer to the daily price series of McDonald’s stock in Exercise 4.8. Instead of looking at the prices themselves, consider now the daily changes in prices found in the provided data file. MCD(a) Using software, plot the price changes over time.Describe
Are McDonald’s prices independent? Over time, stock prices are always on the move. Consider a time series of 1126 consecutive daily prices of McDonald’s stock from the beginning of January 2010 to the near the end of June 2014.1 MCD(a) Using software, plot the prices over time. Are the prices
Random digits. As discussed in Chapter 3, generation of random numbers is one approach for obtaining a simple random sample (SRS). If we were to look at the random generation of digits, the mechanism should give each digit probability 0.1. Consider the digit “0’’ in particular.(a) The table
Credit monitoring. In a recent study of consumers, 25% reported purchasing a credit-monitoring product that alerts them to any activity on their credit report. Suppose you want to use a physical device to simulate the outcome of a consumer purchasing the credit-monitoring product versus the outcome
Financial fraud. It has been estimated that around one in six fraud victims knew the perpetrator as a friend or acquaintance. Financial fraud includes crimes such as unauthorized credit card charges, withdrawal of money from a savings or checking account, and opening an account in someone else’s
Are the trials independent? For each of the following situations, identify the trials as independent or not. Explain your answers.(a) The outside temperature in Chicago at noon on New Year’s Day, each year for the next five years.(b) The number of tweets that you receive on the next 10
Interpret the probabilities. Refer to the previous exercise. In each case, interpret the term “probability’’for the phenomena that are random. For those that are not random, explain why the term “probability’’ does not apply.
Are these phenomena random? Identify each of the following phenomena as random or not. Give reasons for your answers.(a) The outside temperature in Chicago at noon on New Year’s Day.(b) The first character to the right of the “@’’ symbol in an employee’s company email address.(c) You draw
Not just coins. We introduced this chapter with the most recognizable experiment of chance, the coin toss. The coin has two random outcomes, heads and tails. But, this book is not about coin tossing per se. Provide two examples of business scenarios in which there are two distinct but uncertain
Your institutional review board. Your college or university has an institutional review board that screens all studies that use human subjects. Get a copy of the document that describes this board (you can probably find it online).(a) According to this document, what are the duties of the board?(b)
Two ways to ask sensitive questions. Sample survey questions are usually read from a computer screen. In a computer-aided personal interview (CAPI), the interviewer reads the questions and enters the responses. In a computer-aided self interview (CASI), the interviewer stands aside and the
Randomization for testing a breakfast food. To demonstrate how randomization reduces confounding, return to the breakfast food testing experiment described in Example 3.18 (page 146).Label the 30 rats 01 to 30. Suppose that, unknown to the experimenter, the 10 rats labeled 01 to 10 have a genetic
Design your own experiment. The previous two exercises illustrate the use of statistically designed experiments to answer questions of interest to consumers as well as to businesses. Select a question of interest to you that an experiment might answer, and briefly discuss the design of an
Mac versus PC. Many people hold very strong opinions about the superiority of the computer they use. Design an experiment to compare customer satisfaction with the Mac versus the PC. Consider whether or not you will include subjects who routinely use both types of computers and whether or not you
Quality of service. Statistical studies can often help service providers assess the quality of their service. The U.S. Postal Service is one such provider of services. We wonder if the number of days a letter takes to reach another city is affected by the time of day it is mailed and whether or not
The product should not be discolored. Few people want to eat discolored french fries. Potatoes are kept refrigerated before being cut for french fries to prevent spoiling and preserve flavor. But immediate processing of cold potatoes causes discoloring due to complex chemical reactions. The
Experiments and surveys for business.Write a short report describing the differences and similarities between experiments and surveys that would be used in business. Include a discussion of the advantages and disadvantages of each.
Treating drunk drivers. Once a person has been convicted of drunk driving, one purpose of court-mandated treatment or punishment is to prevent future offenses of the same kind. Suggest three different treatments that a court might require. Then outline the design of an experiment to compare their
Student attitudes concerning labor practices. You want to investigate the attitudes of students at your school about the labor practices of factories that make college-brand apparel. You have a grant that will pay the costs of contacting about 500 students.(a) Specify the exact population for your
Attitudes toward collective bargaining.A labor organization wants to study the attitudes of college faculty members toward collective bargaining.These attitudes appear to be different depending on the type of college. The American Association of University Professors classifies colleges as
How much do students earn? A university’s financial aid office wants to know how much it can expect students to earn from summer employment.This information will be used to set the level of financial aid. The population contains 3478 students who have completed at least one year of study but have
Learning about markets. Your economics professor wonders if playing market games online will help students understand how markets set prices. You suggest an experiment: have some students use the online games, while others discuss markets in recitation sections. The course has two lectures, at 8:30
Will the regulation make the product safer? Canada requires that cars be equipped with“daytime running lights,” headlights that automatically come on at a low level when the car is started. Some manufacturers are now equipping cars sold in the United States with running lights. Will running
Questions about attitudes. Write two questions about an attitude that concerns you for use in a sample survey. Make the first question so that it is biased in one direction, and make the second question biased in the opposite direction. Explain why your questions are biased, and then write a third
Does the new product taste better? Before a new variety of frozen muffins is put on the market, it is subjected to extensive taste testing. People are asked to taste the new muffin and a competing brand and to say which they prefer. (Both muffins are unidentified in the test.) Is this an
Executives and exercise. A study of the relationship between physical fitness and leadership uses as subjects middle-aged executives who have volunteered for an exercise program. The executives are divided into a low-fitness group and a high-fitness group on the basis of a physical examination. All
Employee meditation. You see a news report of an experiment that claims to show that a meditation technique increased job satisfaction of employees.The experimenter interviewed the employees and assessed their levels of job satisfaction. The subjects then learned how to meditate and did so
A hot fund. A large mutual funds group assigns a young securities analyst to manage its small biotechnology stock fund. The fund’s share value increases an impressive 43% during the first year under the new manager. Explain why this performance does not necessarily establish the manager’s
Marketing a dietary supplement. Your company produces a dietary supplement that contains a significant amount of calcium as one of its ingredients.The company would like to be able to market this fact successfully to one of the target groups for the supplement:men with high blood pressure. To this
Can you remember how many? An opinion poll calls 2200 randomly chosen residential telephone numbers, and then asks to speak with an adult member of the household. The interviewer asks, “How many movies have you watched in a movie theater in the past 12 months?”(a) What population do you think
Coupons and customer expectations.A researcher studying the effect of coupons on consumers’ expectations makes up two different series of ads for a hypothetical brand of cola for the past year.Students in a family science course view one or the other sequence of ads on a computer. Some students
Compare Pizza Hut with Domino’s. Do consumers prefer pizza from Pizza Hut or from Domino’s? Discuss how you might make this a blind test in which neither source of the pizza is identified.Do you think that your blinding will be successful for all subjects? Describe briefly the design of a
What type of study? What is the best way to answer each of the following questions: an experiment, a sample survey, or an observational study that is not a sample survey? Explain your choices.(a) Are people generally satisfied with the service they receive from a customer call center?(b) Do new
Price promotions and consumer behavior.A researcher is studying the effect of price promotions on consumer behavior. Subjects are asked to choose between purchasing a single case of a soft drink for$4.00 or three cases of the same soft drink for $10.00.Is this study an experiment? Why? What are the
What’s wrong? Explain what is wrong in each of the following statements. Give reasons for your answers.(a) A simple random sample was used to assign a group of 30 subjects to three treatments.(b) It is better to use a table of random numbers to select a simple sample than it is to use a
Confidentiality at NORC. The National Opinion Research Center conducts a large number of surveys and has established procedures for protecting the confidentiality of their survey participants. For its Survey of Consumer Finances, it provides a pledge to participants regarding confidentiality. This
Online behavioral advertising. The Federal Trade Commission Staff Report “Self-Regulatory Principles for Online Behavioral Advertising” defines behavioral advertising as “the tracking of a consumer’s online activities over time—including the searches the consumer has conducted, the
What is wrong? Explain what is wrong in each of the following scenarios.(a) Clinical trials are always ethical as long as they randomly assign patients to the treatments.(b) The job of an institutional review board is complete when they decide to allow a study to be conducted.(c) A treatment that
Deceiving subjects. A psychologist conducts the following experiment: she measures the attitude of subjects toward cheating, then has them play a game rigged so that winning without cheating is impossible.The computer that organizes the game also records—unknown to the subjects—whether or not
Deceiving subjects. Students sign up to be subjects in a psychology experiment. When they arrive, they are told that interviews are running late and are taken to a waiting room. The experimenters then stage a theft of a valuable object left in the waiting room.Some subjects are alone with the
Asking teens about sex. The Centers for Disease Control and Prevention, in a survey of teenagers, asked the subjects if they were sexually active. Those who said “Yes” were then asked, “How old were you when you had sexual intercourse for the first time?” Should consent of parents be
AIDS trials in Africa. One of the most important goals of AIDS research is to find a vaccine that will protect against HIV infection. Because AIDS is so common in parts of Africa, that is the easiest place to test a vaccine. It is likely, however, that a vaccine would be so expensive that it could

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