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Statistics For Business And Economics 13th Edition James T. McClave, P. George Benson, Terry Sincich - Solutions

The tolerance limits for a particular quality characteristic (e.g., length, weight, or strength) of a product are the minimum and/or maximum values at which the product will operate properly. Tolerance limits are set by the engineering design function of the manufacturing operation (Total Quality
The U.S. Army is working with a major defense contractor (not named here for both confidentiality and security reasons) to develop a "super" weapon. The weapon is designed to fire a large number of sharp tungsten bullets-called flechettes-with a single shot that will destroy a large number of enemy
Refer to the NHTSA crash tests of new car models, Exercise 4.3 (p. 193). A summary of the driver-side star ratings for the 98 cars in the file is reproduced in the accompanying Minitab printout. Assume that one of the 98 cars is selected at random and let x equal the number of stars in the car's
A common transportation problem in large cities is congestion on the freeways. In the Canadian Journal of Civil Engineering (January 2013), civil engineers investigated the use of variable speed limits (VSL) to control the congestion problem. A portion of an urban freeway was divided into three
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 2.3. Recall that in a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63
A team of industrial management university professors investigated the reliability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems Engineering, March 2013). An example of such a network is a system for producing integrated circuit (IC)
According to the Earth Policy Institute (July 2014), 65% of the world's solar energy cells are manufactured in China. Consider a random sample of five solar energy cells and let x represent the number in the sample that are manufactured in China. In the next section, we show that the probability
USDA chicken inspection. In Exercise 3.19 (p. 146) you learned that one in every 100 slaughtered chickens passes USDA inspection with fecal contamination. Consider a random sample of three slaughtered chickens that all pass USDA inspection. Let x equal the number of chickens in the sample that have
Refer to The Journal of Finance (December 2011) study of whether the decision to invest in the stock market is dependent on IQ, Exercise 3.46 (p. 158). Recall that an IQ score (from a low score of 1 to a high score of 9) was determined for each in a sample of 158,044 Finnish citizens. Also recorded
Refer to the Canadian Journal of Civil Engineering (January 2013) study of variable speed limits, Exercise 4.23 (p. 201). Recall that a portion of an urban freeway was divided into three sections of equal length, and variable speed limits were posted (independently) in each section. The probability
A "Condorcet" committee of, say, 3 members, is a committee that is preferred by voters over any other committee of 3 members. A scoring function was used to determine "Condorcet" committees in Mathematical Social Sciences (November 2013). Consider a committee with members A, B, and C. Suppose there
Working on summer vacation. Recall (Exercise 3.13, p. 145) that a Harris Interactive (July 2013) poll found that 22% of U.S. adults do not work at all while on summer vacation. In a random sample of 10 U.S. adults, let x represent the number who do not work during summer vacation.a. For this
Some grocery stores now offer their customers a free loyalty card that will save money on their purchases. In exchange, the store will keep track of the customer's shopping habits and could potentially sell these data to third parties. A Pew Internet & American Life Project Survey (January
The Physicians' Foundation reported that 58% of all general practice physicians in the United States do not recommend medicine as a career (The Physicians' Foundation 2012 Survey of America's Physicians). Let x represent the number of sampled general practice physicians who do not recommend
Does participation in youth and/or high school sports lead to greater wealth later in life? This was the subject of a recent Harris POLL (March 2015). The poll found that 15% of adults who participated in sports now have an income greater than $100,000. In comparison, 9% of adults who did not
Refer to the Psychological Science (August 2011) study of fingerprint identification, Exercise 3.85. The study found that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 92% of the time. In contrast, a novice will correctly identify the
Refer to the Chance (Fall 2007) study on making your vote count, Exercise 3.29. Recall the scenario where you are one of five county commissioners voting on an issue, and each commissioner is equally likely to vote for or against.a. Your vote counts (i.e., is the decisive vote) only if the other
Give an example of a discrete random variable that would be of interest to a banker.
A network forensic analyst is responsible for identifying worms, viruses, and infected nodes in the computer network. A new methodology for finding patterns in data that signify infections was investigated in IEEE Transactions on Information Forensics and Security (May, 2013). The method uses
Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 4.25. The study found that of 106 social robots, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor
Over the past 5 years, U.S. airlines average about 1 fatality per month (U.S. Department of Transportation, National Transportation Statistics: 2015).Assume that the probability distribution for x, the number of fatalities per month, can be approximated by a Poisson probability distribution.a. What
Refer to the investigation of contaminated gun cartridges at a weapons manufacturer, presented in Exercise 4.29. In a sample of 158 cartridges from a certain lot, 36 were found to be contaminated and 122 were "clean." If you randomly select 5 of these 158 cartridges, what is the probability that
Hotel management. Give an example of a discrete random variable that would be of interest to the manager of a hotel.
A study of the arrival process of people using elevators at a multilevel office building was conducted and the results reported in Building Services Engineering Research and Technology (October 2012). Suppose that at one particular time of day, elevator passengers arrive in batches of size 1 or 2
With a variable life insurance policy, the rate of return on the investment (i.e., the death benefit) varies from year to year. A study of these variable return rates was published in International Journal of Statistical Distributions (Vol. 1, 2015). A transformed ratio of the return rates (x) for
Refer to the Journal of Vacation Marketing (January 2016) study of travelers' familiarity with ecolabels used by hotels, Exercise 2.64 (p. 80). Recall that adult travelers were shown a list of 6 different ecolabels, and asked, "Suppose the response is measured on a continuous scale from 10 (not
Refer to the Electrical Engineering (Vol. 95, 2013) study of the power quality (sags and swells) of a transformer, Exercise 2.76 (p. 86). For transformers built for heavy industry, the distribution of the number of sags per week has a mean of 353 with a standard deviation of 30. Of interest is x̅,
According to the most recent Global Business Travel Association (GBTA) survey, the average base salary of a U.S. travel management professional is $94,000. Assume that the standard deviation of such salaries is $30,000. Consider a random sample of 50 travel management professionals and let x
Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 1.28 (p. 27). Corporate sustainability, recall, refers to business practices designed around social and environmental considerations. The level of support senior managers have for
Refer to the International Journal of Statistical Distributions (Vol. 1, 2015) study of a variable life insurance policy, Exercise 4.97 (p. 238). Recall that a ratio (x) of the rates of return on the investment for two consecutive years was shown to have a normal distribution, with μ = 1.5 and σ
Factors (May 2014) published the results of a study designed to determine whether video game players are better than non-video game players at crossing the street when presented with distractions. Participants (college students) entered a street-crossing simulator. The simulator was designed to
University of Louisville researchers examined the process of filling plastic pouches of dry blended biscuit mix (Quality Engineering, Vol. 91, 1996). The current fill mean of the process is set at μ = 406 grams, and the process fill standard deviation is σ = 10.1 grams. (According to the
According to a recent Pew Research Center Survey (December 2015), 15% of U.S. adults admitted they are "cord cutters," i.e., they canceled the cable/satellite TV service they once subscribed to. In a random sample of 500 U.S. adults, let p̂ represent the proportion who are "cord cutters."a. Find
Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, The researchers obtained a random sample of 106 social robots through a Web search and determined the number that were designed with legs, but no wheels. Let p̂ represent
According to a Harris Interactive (July 2013) poll of U.S. adults, about 60% work during their summer vacation. Assume that the true proportion of all U.S. adults who work during summer vacation is p = .6. Now consider a random sample of 500 U.S. adults.a. What is the probability that between 55%
According to an Occupational and Health Safety Administration (OHSA) 2014 report, a hospital is one of the most dangerous places to work. The major cause of injuries that result in missed work was overexertion. Almost half (48%) of the injuries that result in missed work were due to overexertion.
Refer to the results of the 2015 North American Hotel Guest Satisfaction Index Study, Exercise 4.49 (p. 215). Recall that 15% of hotel guests were "delighted" with their experience (giving a rating of 10 out of 10); of these guests, 80% stated they would "definitely" recommend the hotel. In a
Refer to The Journal of Finance (December 2011) study of whether the decision to invest in the stock market is dependent on IQ, Exercise 3.46 (p. 158). The researchers found that the probability of a Finnish citizen investing in the stock market differed depending on IQ score. For those with a high
Refer to the Psychological Science (August 2011) study of fingerprint identification. Recall that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 92% of the time. Consider a forensic database of 1,000 different pairs of fingerprints, where
As part of a study on income tax compliance (Behavioral Research and Accounting, January 2015), researchers found that 37% of adult workers prepare their own tax return. Assume that this percentage applies to all U.S. adult workers. Now consider a random sample of 270 adult workers. a. Find the
In a survey titled U.S. Smartphone Use in 2015, 90% of smartphone users indicated that they have had a problem with a downloaded application (app) on their cell phone not working correctly. Assume this percentage applies to all smartphone users in the United States. In a random sample of 75
As with all sample statistics, A is computed by utilizing a specified function (formula) of the sample measurements. (For example, if A were the sample mean, the specified formula would sum the measurements and divide by the number of measurements.)a. Describe what we mean by the phrase "the
A random sample of n = 68 observations is selected from a population with μ = 19.6 and σ = 3.2. Approximate each of the following probabilities: a. P(x̅ ≤ 19.6) b. P(x̅ ≤ 19) c. P(x̅ ≥ 20.1) d. P(19.2 ≤ x̅ ≤ 20.6)
Refer to the Chance (Winter 2001) examination of Scholastic Assessment Test (SAT) scores of students who pay a private tutor to help them improve their results. On the SAT-Mathematics test, these students had a mean score change of +19 points, with a standard deviation of 65 points. In a random
Refer to Exercise 4.173 and the August 2011 survey by the Pew Internet & American Life Project. The study found that 40% of adult cell phone owners have downloaded an application ("app") to their cell phone. Assume this percentage applies to the population of all adult cell phone owners. a. In a
Refer to the Anti-Corrosion Methods and Materials (Vol. 50, 2003) study of the surface roughness of oil field pipes, Exercise 2.46. Recall that a scanning probe instrument was used to measure the surface roughness x (in micrometers) of 20 sampled sections of coated interior pipe. Consider the
Lead time is the time between a retailer placing an order and having the product available to satisfy customer demand. It includes time for placing the order, receiving the shipment from the supplier, inspecting the units received, and placing them in inventory. Interested in average lead time, m,
Refer to Exercise 5.68. The mean diameter of the bearings produced by the machine is supposed to be .5 inch. The company decides to use the sample mean from Exercise 5.68 to decide whether the process is in control (i.e., whether it is producing bearings with a mean diameter of .5 inch). The
Banks that merge with others to form "mega-banks" sometimes leave customers dissatisfied with the impersonal service. A poll by the Gallup Organization found 20% of retail customers switched banks after their banks merged with another. One year after the acquisition of First Fidelity by First
A manufacturer produces safety jackets for competitive fencers. These jackets are rated by the minimum force, in newtons, that will allow a weapon to pierce the jacket. When this process is operating correctly, it produces jackets that have ratings with an average of 840 newtons and a standard
A large number of preventable errors (e.g., overdoses, botched operations, misdiagnoses) are being made by doctors and nurses in U.S. hospitals. A study of a major metropolitan hospital revealed that of every 100 medications prescribed or dispensed, 1 was in error, but only 1 in 500 resulted in an
A building contractor has decided to purchase a load of factory-reject aluminum siding as long as the average number of flaws per piece of siding in a sample of size 35 from the factory's reject pile is 2.1 or less. If it is known that the number of flaws per piece of siding in the factory's reject
Find za/2 for each of the following: a. α = .10 b. α = .01 c. α = .05 d. α = .20
Are police officers susceptible to higher-than-normal heart rates? The heart rate variability (HRV) of police officers was the subject of research published in the American Journal of Human Biology (January 2014). HRV is defined as the variation in time intervals between heartbeats. A measure of
Refer to the Chance (Summer 2007) study of an actual phishing attack against an organization, Exercise 5.33. Recall that phishing describes an attempt to extract personal/financial information from unsuspecting people through fraudulent e-mail. The interarrival times (in seconds) for 267 fraud box
In each of the following instances, determine whether you would use a z- or t-statistic (or neither) to form a 95% confidence interval and then look up the appropriate z- or t-value. a. Random sample of size n = 23 from a normal distribution with unknown mean m and standard deviation σ b. Random
Online "daily deal" sites (e.g., Groupon) offer customers a voucher to purchase a product at discount prices. However, the number of voucher purchases must exceed a predetermined number before the deal becomes active. This key number is termed the "tipping point" in marketing. Characteristics of
Both Delta Airlines and USAir filed for bankruptcy. A study of the impact of bankruptcy on the fares charged by U.S. airlines was published in Research in Applied Economics (Vol. 2, 2010). The researchers collected data on Orlando-bound airfares for three airlines-Southwest (a stable airline),
Budget lapsing occurs when unspent funds do not carry over from one budgeting period to the next. Refer to the Journal of Management Accounting Research (Vol. 19, 2007) study on budget lapsing at U.S. Army hospitals, Exercise 2.113. Because budget lapsing often leads to a spike in expenditures at
Refer to Exercise 2.158 and the Journal of Statistics Education data on diamonds saved in the accompanying file. Consider the quantitative variable, number of carats, recorded for each of the 308 diamonds for sale on the open market. a. Select a random sample of 30 diamonds from the 308
Refer to the Anti-corrosion Methods and Materials (Vol. 50, 2003) study of the surface roughness of coated interior pipe used in oil fields, Exercise 2.4. The data (in micrometers) for 20 sampled pipe sections are reproduced in the accompanying table; a Minitab analysis of the data appears below.a.
The costs associated with conducting interviews for a job opening have skyrocketed over the years. According to a Harris Interactive survey, 211 of 502 senior human resources executives at U.S. companies believe that their hiring managers are interviewing too many people to find qualified
Airlines overbook flights in order to reduce the odds of flying with unused seats. An article in Transportation Research (Vol. 38, 2002) investigated the optimal overbooking policies for major airlines. One of the variables measured for each airline was the compensation (in dollars) per bumped
Refer to the American Economic Review (December 2008) study of college dropouts, Exercise 2.79. Recall that one factor thought to influence the college dropout decision was expected GPA for a student who studied 3 hours per day. In a representative sample of 307 college students who studied 3 hours
Methyl t-butyl ether (MTBE) is an organic water contaminant that often results from gasoline spills. The level of MTBE (in parts per billion) was measured for a sample of 12 well sites located near a gasoline service station in New Jersey (Environmental Science & Technology, January 2005). The
Studies have shown that drivers who use cell phones while operating a motor passenger vehicle increase their risk of an accident. Nevertheless, drivers continue to make cell phone calls while driving. A June 2011 Harris Poll of 2,163 adults found that 60% (1,298 adults) use cell phones while
Sampling of Medicare and Medicaid claims by the federal and state agencies who administer those programs has become common practice to determine whether providers of those services are submitting valid claims. (See the Statistics in Action for this chapter.) The reliability of inferences based on
Interfaces (March-April 1995) presented the case of a ship that fishes for scallops off the coast of New England. In order to protect baby scallops from being harvested, the U.S. Fisheries and Wildlife Service requires that "the average meat per scallop weigh at least 1/36 of a pound." The ship was
Refer to Exercise 4.126 (p. 246) and the study of the wear-out failure time of used colored display panels purchased by an outlet store. Recall that prior to acquisition; the panels had been used for about one-third of their expected lifetimes. The failure times (in years) for a sample of 50 used
How complicit are entry-level accountants in carrying out an unethical request from their superiors? This was the question of interest in a study published in the journal Behavioral Research in Accounting (July 2015). A sample of 86 accounting graduate students participated in the study. After
The day after Thanksgiving-called Black Friday-is one of the largest shopping days in the United States. Winthrop University researchers conducted interviews with a sample of 38 women shopping on Black Friday to gauge their shopping habits and reported the results in the International Journal of
Refer to the Glassdoor Economic Research (August 25, 2015) report on salaries of executives and workers at S&P 500 firms. Recall that the data file contains the salaries (in $ millions) of the 441 CEOs who participated in the survey. Suppose you are interested in estimating the mean salary for
Named for the section of the Internal Revenue Code that authorized them, 401(k) plans permit employees to shift part of their before-tax salaries into investments such as mutual funds. One company, concerned with what it believed was a low employee participation rate in its 401(k) plan, sampled 30
What is the confidence level of each of the following confidence intervals for μ? a. x̅ ± 1.96 (σ/√n) b. x̅ ± 1.645 (σ/√n) c. x̅ ± 2.575 (σ/√n) d. x̅ ± 1.282 (σ/√n) e. x̅ ± .99 (σ/√n)
In Psychological Science (Vol. 22, 2011), researchers reported that a chief executive officer's facial structure can be used to predict a firm's financial performance. The study involved measuring the facial width to-height ratio (WHR) for each in a sample of 55 CEOs at publicly traded Fortune 500
Refer to the Chance (Winter 2001) and National Education Longitudinal Survey (NELS) study of 265 students who paid a private tutor to help them improve their SAT scores, Exercise 2.88 (p. 89). The changes in both the SAT-Mathematics and SAT-Verbal scores for these students are reproduced in the
Explain the differences in the sampling distributions of x̅ for large and small samples under the following assumptions.a. The variable of interest, x, is normally distributed.b. Nothing is known about the distribution of the variable x.
The following random sample was selected from a normal distribution: 4, 6, 3, 5, 9, 3.a. Construct a 90% confidence interval for the population mean m.b. Construct a 95% confidence interval for the population mean m.c. Construct a 99% confidence interval for the population mean m.d. Assume that the
An observational study of teams fishing for the red spiny lobster in Baja California Sur, Mexico, was conducted and the results published in Bulletin of Marine Science (April 2010). One of the variables of interest was the average distance separating traps-called trap spacing-deployed by the same
Many ancient Egyptian tombs were cut from limestone rock that contained uranium. Since most tombs are not well ventilated, guards, tour guides, and visitors may be exposed to deadly radon gas. In Radiation Protection Dosimetry (December 2010), a study of radon exposure in tombs in the Valley of
Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study on the current trend in the design of social robots, Exercise 2.78. Recall that in a random sample of social robots obtained through a Web search, 28 were built with wheels. The accompanying table shows the number of
Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. The average LOS in the United States is 4.5 days (Healthcare Cost and Utilization Project Statistical Brief, October 2014). A random sample of 20
Refer to the IHS Journal of Hydraulic Engineering (September 2012) study of commercial pipes used in a water distribution network, Exercise 2.124. Of interest was the ratio of repair to replacement cost of the pipe. The ratios for a sample of 13 different pipe sizes are listed in the next table.
A new formula for estimating the water evaporation from occupied swimming pools was proposed and analyzed in the journal Heating/ Piping/Air Conditioning Engineering (April 2013). The key components of the new formula are number of pool occupants, area of pool's water surface, and the density
Molten salt is used in an electro-refiner to treat nuclear fuel waste. Eventually, the salt needs to be purified (for reuse) or disposed of. A promising method of purification involves oxidation. Such a method was investigated in Chemical Engineering Research and Design (March. 2013). An important
In Exercise 2.44 you learned that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The table below lists the annualized percentage return on investment (as compared to the Standard & Poor's 500 Index) for 13 randomly
Refer to the Journal of Petroleum Geology (April 2010) study of the environmental factors associated with biodegradation in crude oil reservoirs, Exercise 2.29. One indicator of biodegradation is the level of dioxide in the water. Recall that 16 water specimens were randomly selected from various
IPOs-initial public offerings of stock-create billions of dollars of new wealth for owners, managers, and employees of companies that were previously privately owned. Nevertheless, hundreds of large and thousands of small companies remain privately owned. The revenues of a random sample of 15 firms
Describe the sampling distribution of p̂ based on large samples of size n-that is, give the mean, the standard deviation, and the (approximate) shape of the distribution of p̂ when large samples of size n are (repeatedly) selected from the binomial distribution with probability of success p.
For the binomial sample information summarized in each part, indicate whether the sample size is large enough to use the methods of this chapter to construct a confidence interval for p.a. n = 400, p̂ = .10b. n = 50, p̂ = .10c. n = 20, p̂ = .5d. n = 20, p̂ = .3
A random sample of size n = 121 yielded p̂ = .88. a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p? Explain. b. Construct a 90% confidence interval for p. c. What assumption is necessary to ensure the validity of this confidence
A random sample of size n = 225 yielded p̂ = .46.a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p? Explain.b. Construct a 95% confidence interval for p.c. Interpret the 95% confidence interval.d. Explain what is meant by the phrase "95%
Customers who participate in a store's free loyalty card program save money on their purchases but allow the store to keep track of their shopping habits and potentially sell these data to third parties. A Pew Internet & American Life Project Survey (January 2016) revealed that half (225) of a
Studies have shown that drivers who use cell phones while operating a motor passenger vehicle increase their risk of an accident. To quantify this risk, the New England Journal of Medicine (January 2, 2014) reported on the risk of a crash (or near crash) for both novice and expert drivers when
Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots. Exercise 5.44, The researchers obtained a random sample of 106 social robots through a Web search and determined that 63 were designed with legs, but no wheels. a. Find a
The Minneapolis Star Tribune (August 12, 2008) reported that 73% of Americans say that Starbucks coffee is overpriced. The source of this information was a national telephone survey of 1,000 American adults conducted by Rasmussen Reports.a. Identify the population of interest in this study.b.
A random sample of 70 observations from a normally distributed population possesses a sample mean equal to 26.2 and a sample standard deviation equal to 4.1. a. Find an approximate 95% confidence interval for μ. b. What do you mean when you say that a confidence coefficient is .95? c. Find an
The International Nanny Association (INA) reports that in a sample of 928 in-home child care providers (nannies), 128 have passed the INA Nanny Credential Exam (2014 International Nanny Association Salary and Benefits Survey). Use Wilson's adjustment to find a 95% confidence interval for the true
Refer to the State of Cyber security (2015) survey of firms from around the world. Recall that of the 766 firms that responded to the survey, 628 (or 82%) expect to experience a cyber attack (e.g., a Malware, hacking, or phishing attack) during the year. Estimate the probability of an expected
Refer to the Behavioral Research and Accounting (January 2015) study on income tax compliance, Exercise 5.50. Recall that in a sample of 270 U.S. adult workers, the researchers found that 37% prepare their own tax return. a. Construct a 99% confidence interval for the true proportion of all U.S.

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