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Questions and Answers of
Statistics
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.
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
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.
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
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
A team of industrial management university professors investigated the reliability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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 ≥
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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,
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%
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
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
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
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
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
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
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
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
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
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