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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

According to Forbes (Jan. 11,1999), retailing was one of the U.S. economy's best-performing sectors in 1998. The Internet and its associated on-line sales played a significant role in the
Discuss the conditions under which the median is preferred to the mean as a measure of central tendency.
Consider the following three measurements: 50, 70, 80. Find the z-score for each measurement if they are from a population with a mean and standard deviation equal toa. p = 60, u = 10b. p = 50, u =
If the range of a set of data is 20, find a rough approximation to the standard deviatmn ot the data sct.
For each of the following data sets, compute i, s2, and s:a. 13,1,10,3,3b. 13,6,6,0c. 1,0,1,10,11,11,15d. 3,3,3,3
For each of the following data sets, compute i, s2, and s. If appropriate, specify the un~ts in which your answers are expressed.a. 4,6,6,5,6,7b. -$I, $4, -$3, $0, -$3, -$6c. %%,%%,2/5%, 1/5%, Xh%,d.
A manufacturer of industrial wheels is losing many profitable orders because of the long time it takes the firm's marketing, engineering, and accounting departments to develop price quotes for
A time series plot similar to the one shown here appeared in a recent advertisement for a wellknown golf magazine. One person might interpret the plot's message as the longer you subscribe to the
A company has roughly the same number of people in each of fivc departments: Production, Sales, R&D, Maintenance, and Administration. The following table lists the number and type of major injuries
The accompanying table lists the unemployment rate in 1997 tor a sample of nine countries.a. Find the mean and median unemployment rate in the sample. Interpret these values.b. Find the standard
Forbes magazine (Jan. 11,1999) reported the financial standings of each team in the National Football League (NFL). The next table lists current team value (without deduction for debt, except stadium
A study by the U.S. Public Research Interest Group found that in Massachusetts bank customers were charged lower fees than the national average for regular checking accounts, NOW accounts, and
The U.S. Federal Trade Commission has recently begun assessing fines and other penalties against weight-loss clinics that make unsupported or misleading claims about the effectiveness of their
The Baltimore Orioles had the highest player payroll in Major League Baseball (MLB) in 1998 while the Tampa Bay Devil Rays (an expansion team) had one of the lowest payrolls. The 1998 salaries for
The Age Discrimination in Employment Act mandates that workers 40 years of age or older be treated without regard to age in all phases of employment (hiring, promotions, firing, etc.). Age
A national chain of automobile oil-change franchises claims that "your hood will be open for less than 12 minutes when we service your car." To check their claim, an undercover consumer reporter from
Construct a time series plot for these data and describe in words what it reveals.The automobile sales in the United States (in thousands of cars) for the "Big Three" U.S. manufacturers (Ford,
Computer anxiety is defined as "the mixture of fear, apprehension, and hope that people feel when planning to interact, or when interacting with a computer." Researchers have found computer anxiety
An experiment results in one of the followmg sample points: E,, E,, E,, E,, or E,.a. Find P(EJ ~f P(E,) = .I, P(E,) = .2, P(E,) = .I, and P(E5) = .l. pi- - 5b. Find P(E,) ~f P(E,) = P(E,), P(E ) -
The accompanymg diagram describes the sample space of a particular experiment and events A and B.a. What is this type of diagram called?b. Suppose the sample points are equally likely.Find P(A) and
The sample space for an experiment contains five sample points with probabilities as shown in the table. Find the probability of each of the following events:Sample Points Probabilities 1, .05 2 .20
Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. Determinc the probability of observing each of the following cvcnts:A: {Two blue
Total Quality Management (TQM) has been defined as responsive customer service through continuously improved and redesigned work processes (Quality Progress, July 1995). However, as its usage has
Communications products (telephones, fax machines, etc.) can be designed to operate on either an analog or a digital system. Because of improved accuracy, a digital signal will soon replace the
Of six cars produced at a particular factory between 8 and 10 A.M. last Monday morning, test runs revealed three of them to be "lemons."Nevertheless, three of the six cars were shipped to dealer A
Carbon monoxide (CO) is an odorless, colorless, highly toxic gas which is produced by fires as well as by motor vehicles and appliances that use carbon-based fuels. The Anterican Journal of Public
The credit card industry depends heavily on mail solicitation to attract new customers. In 1994, the industry sent out 2.4 billion pieces of mail and incurred postage costs of ncarly $500
Consumer Reports magazine annually asks readers to evaluate their experiences in buying a new car during the previous year. More than 120.000 questionnaires were completed for the 1994 sales year.
Often, probabilities are expresscd in terms of odds. especially in gambling settings. For example, handicappers for greyhound races express their belief about the probabilities that each greyhound
The Value Line Survey, a service for common stock investors, provides its subscribers with upto-date evaluations of the prospects and risks associated with the purchase of a large number of common
Sustainable development or sustainable farming means "finding ways to live and work the Earth without jeopardizing the future" (Schmickle, Minneapolis Star Tribune, June 20, 1992). Studies were
A fair coin is tossed three times and the events A V and B are defined as follows:A: (At least onc hcad is observed]B: (The number of heads observed is odd]a. Identify the sample points in the events
A pair of fair dice is tossed. Define the following events:A: {You will roll a 7) (i.e., the sum of the dots on the up faces of the two dice is cqual to 7)B: {At least one of the two dice shows a
Consider the accompanying Venn diagram, whcrc P(E,) = P(E,) = P(E,) = %. P(E,) = P(E,) =%o, P(E,) = %o, and P(E,) = 1/5. Find each of the following probabilities:
Consider the accompanying Venn diagram. where P(E,) = .10. P(E,) = .05. P(E,) = P(E,) = .2, P(EJ = .06, P(E,) = .3, P(E,) = .06, and P(E,) =.03. Find the following probabilities:a. P(AC)b. P(B')c.
The following table describes the adult population of a small suburb of a large southern city. A marketing research firm plans to randomly select onc adult from the suburb to evaluate a new food
Refer to Exercise 3.21. Use the same event definitions to do the following exercises.a. Write the event that the person selected is under 25 with an income over $50.000 as an intersection of two
A state energy agency mailed questionnaires on energy conservation to 1.000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an esperiment consists of randomly
Corporate downsizing in the United States has caused a significant increase in the demand for temporary and part-time workers. In Japan a sinlilar increase in demand has been fueled by the need for
A buyer for a large metropolitan department store must choose two firms from the four available to supply the store's fall line of men's slacks.The buyer has not dealt with any of the four firms
Roulette is a very popular game in many American casinos. In roulette, a ball spins on a circular wheel that is divided into 38 arcs of equal length, bearing the numbers 00, 0, 1, 2, ..., 35, 36. The
After completing an inventory of three warehouses, a manufacturer of golf club shafts described its stock of 20,125 shafts with the percentages given in the table. Suppose a shaft is selected at
Refer to Exercise 3.27. Define the characteristics of a golf club shaft portrayed by the following events, and then find the probability of each. For each union, use the additive rule to find the
The types of occupations of the 123,060,000 employed workers (age 16 years and older) in the United States in 1994 are described in the table, and their relative frequencies are listed. A worker is
The long& success of a business depends on its ability to market products with superior characteristics that maximize consumer satisfaction and that give the firm a competitive advantage(Kotler,
Identifying managerial prospects who are both talented and motivated is difficult. A humanresources director constructed the following twoway table to define nine combinations of talentmotivation
An experiment results in one of three mutually exclusive events. A, B, or C. It is known that P(A) =.30, P(B) = .55, and P(C) = .15. Find each of the following probabilities:a. P(Au B)b. P(A nC) Ic.
Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E,) = .20, P(E,) = .30,
Three fair coins are tossed and the following events are defined:A: (Observe at least one head]B: (Observe exactly two heads)C: {Observe exactly two tails]D: {Observe at most one head}a. Sum the
An experiment results in one of five sample points with the following probabilities: P(E,) = .22, P(EJ= 31, P(E,) = .15, P(EJ = .22, and P(E,) = .1.The following events have been defined:A: {El, EJ
A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probabilities of the sample points area. Which pairs of events, if any, are mutually exclusive?
For two events, A and B, P(A) = .4 and P(B) = .2.a. Il' A and B are independent, find P(AnR), P(A I B). and P(A U B).b. If A and B are dependent, with P(AJB) = .6, find P(AnB) and P(BA).Applying the
"Go" is one of the oldest and most popular strategic board games in the world, especially in Japan and Korea. This two-player gamc is played on a flat surface marked with 19 vertical and 19 hori
. Businesses that offer credit to their customers are inevitably faced with the task of collecting unpaid bills. A study of collection remedies used by creditors was published in the Journal of
In the last decade, increasingly more employees have been offered a variety of health care plans to choose from. This is a direct result of the growing prevalence of preferred provider
Refer to the American Journal of Public Health study of unintentional carhon monoxide (CO)poisonings in Colorado, Exercise 3.10. The 981 cases were classified in a table, which is reproduced below. A
Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects.
A soft-drink bottler has two quality control inspectors independently check each case of soft dunks lor chipped or cracked bottles before the cases leave the bottling plant. Having observed the work
The table describes the 63.1 million U.S. longform federal tax returns filed with the Internal Revenue Service (IRS) in 1992 and the percentage of those returns that were audited by the IRS.a. If a
"Channel One" is an education television network that is available to all secondary schools in the United States. Participating schools are equipped with TV sets in every classroom in order to
In October 1994. a flaw was discovered in the Pentium chip installed in many new personal computers.The chip produced an incorrect result when dividing two numbers. Intel, the manufacturer of the
The genet~c origin and properties of maize(modern-day corn), a domest~c plant developed 8.000 years ago in Mexico, wai mvestigated in Econornlc Botany (Jan.-Mar. 1995). Seeds from maize ears carry
A particular automatic sprinkler system for highrise apartment buildings, office buildings. and hotels has two different types of activation devices for each sprinkler head. One type has a
Suppose you wish to sample n = 2 elements from a total of N = 10 elements.a. Count the number of different samples that can be drawn, first by listing them, and then by using combinatorial
Suppose you wish to sample n = 3 elements from a total of N = 600 elements.a. Count the number of different samples by using combinatorial mathematics (see Section 3.1).b. If random sampling is to be
Suppose that a population contains N = 200,000 elements. Use a computer or Table I of Appendix B to select a random sample of n = 10 elements from the population. Explain how you selected your
In auditing a firm's financial statements, an auditor will (I) assess the capability of the firm's accounting system to accumulate, measure, and synthesize transactional data properly, and (2) assess
To ascertain the effectiveness of their advertising campaigns, firms frequently conduct telephone interviews with consumers.They may use random samples of telephone numbers that are arbitrarily or
When a company sells shares of stock to investors, the transaction is said to take place in the prinzary nznrket. To enable investors to rescll the stock when they wish, secondary markets called
In addition to its decennial enumeration of the population, the US. Bureau of the Census regularly samples the population to estimate level of and changes in a number of other attributes, such as
What are the two rules that probabilities assigned to sample points must obey?
Are mutually exclusive events also dependent events? Explain.
Given that P(AnB) = .4 and P(AJB) = .8. find P(B). - 5
Which of the following pairs of events are mutually exclus~ve? Justify your response.a. {The Dow Jones Industrial Average increases on Monday). (A large New York bank decreases its prime interest
The accompanying Venn diagram illustrates a sample space containing six sample points and three events. A. B, and C. The orobabilities of the ...sample points are: P(l) = .3, P(2) = .2, P(3) = .1
Two events, A and B, are independent, with P(A)= .3 and P(B) = .l.a. Are A and B mutually exclusive? Why?b. Find P(AI B) and P(B~A).c. Find P(A U B).
Find the numerical value of:
A random sample of five graduate students is to be selected from 50 MBA majors for participation in a case competition.a. In how many different ways can the sample be drawn?b. Show how the random
A research and development company survcycd all 200 of its employees over the age of 60 and obtained the information given in the table below.One of these 200 employees is selected at random.What is
Many US. manufacturers are adopting the IS0 9000 series of standards for setting up and documenting quality systems, processes. and procedures. However, it is not generally known how managers who
The table on page 156 lists the overall percentage of domestic flights of major U.S. airlines that arrived on time during June 1995.a. One of these ten airlines is to be selected at random. What is
The state legislature has appropriated $1 million to be distributed in the form of grants to individuals and organi7ations engaged in the research and development of alternative energy sourccs. You
A manufacturer of electronic digital watches claims that the probability of its watch running more than 1 minute slow or I minute fast after 1 year of use is ,051. A consumer protection agency has
Two marketing research companies, Richard Saunders International and Marketing Intelligence Service. joined forces to create a consumer preference poll called Acupoll. Acupoll is used to predict
Use your intuitive understanding of independence to form an opinion about whether each of the followins scenarios represents an independent event.a. The results of consecutive tosses of a coinb. The
A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club
Insurance companies use rnorrality tables to help them determmc how large a premium to charge a particular individual for a particular life insurance policy. The accompanying table shows the
"What are the characteristics of families with young children (under age 6)?" This was one of several questions posed by a University of Michigan researcher in Children and Youth Services Review
All-terrain vehicles (ATVs) came under fire in the 1980s owing to the high number of injuries and deaths attributed to these machines. In response, manufacturers agreed to provide extensive safety
The perfol-mance of quality inspectors affects both the quality of outgoing products and the cost of the products. A product that passes inspection is assumed to meet quality standards; a product
The figure shown above is a schematic representation of a system comprised of three components.The system operates properly only if all three components operate properly. The three components are
The figure below is a representation of a system comprised of two subsystems that are said to operate in parallel. Each subsystem has two components that operate in series (refer to Exercise
Consider the population of new savings accounts opened in one business day at a bank, as shown in the table. Suppose you wish to draw a random sample of two accounts from this population.Account
Two hundred shoppcrs at a large suburban mall were asked two questions: (1) Did you see a television ad for the sale at department store X during the past two weeks? (2) Did you shop at department
The National Resident Matching Program(NRMP) is a service provided by the Association of American Medical Colleges to match graduating medical students with residency appointments at hospitals. After
A small brewery has two bottling machines.Machine A produces 75% of the bottles and machine B produces 25%. One out of every 20 bottles filled by A is rejected for some reason, while one out of every
Suppose there are 500 applicants for five equivalent positions at a factory and the company is able to narrow the field to 30 equally qualified applicants. Seven of the finalists are minority
A fair coin is flipped 20 times and 20 heads are observed. In such cases it is often said that a tail is due on the next flip. Is this statement true or false? Explain.
If a population data set is normally distributed, what is the proportion of measurements you would expect to fall within the following intervals?a. m { sb. m { 2sc. m { 3s
Normal probability plots for three data sets are shown on the next page. Which plot indicates that the data are approximately normally distributed?

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