?Steel rod quality. In his essay “Making Things Right,” W. Edwards Deming considered the

Refer to the Museum Management and Curatorship (June 2010) study of how museums evaluate their performance, Exercise 2.14 (p. 50). Recall that managers of 30 museums of contemporary art identified the performance measure used most often. A summary of the results is reproduced in the table. Consider the bar graph shown. Identify two ways in which the bar graph might mislead the viewer by overemphasizing the importance of one of the performance measures.

Refer to the Significance (December 2015) study on estimating the number of U.S, deaths attributable to nitrogen oxide (NOx) pollution produced from illegal VW vehicles, Exercise 2.82 (p. 87). Recall that the researchers computed the estimate for each of 27 different scenarios involving different values of three variables: total distance (in miles) driven by these illegal VW vehicles, the amount by which the VW vehicles exceeded the EPA standard for NOx, and the estimated association between NOx emissions and mortality. Summary statistics for the estimated number of deaths are shown in the accompanying Minitab printout. Suppose the media have requested that the researchers provide a single statistic that best represents the center of the distribution of estimated deaths attributable to NOx pollution produced from the illegal VW vehicles. This statistic will be used to publicize the study findings. a. If you work for Volkswagen and would like to diffuse the media’s reaction to the emissions scandal, which statistic would you choose to report and why? b. If you support an environmental watch group and would like to incite the media to publicize the emissions scandal, which statistic would you choose to report and why?

Consider the following graphic, similar to one produced by the Silicon Alley Insider, an online publication for business news. The graph is attempting to show the increasing trend in annual revenue produced by Craigslist as compared to the decrease in newspaper classified ad sales. a. Why might the graph be misleading? [Hint: Focus on the units of measure on the two vertical axes.] b. Redraw the graph, but use the same units of measure for both Craigslist revenue and newspaper ad sales. What conclusions can you draw from the redrawn graph?

In the summer of 2010, an explosion on the Deepwater Horizon oil drilling rig caused a leak in one of British Petroleum (BP) Oil Company’s wells in the Gulf of Mexico. Crude oil rushed unabated for 3 straight months into the Gulf until BP could fix the leak. During the disaster, BP used suction tubes to capture some of the gushing oil. In May of 2011, in an effort to demonstrate the daily improvement in the process, a BP representative presented a graphic on the daily number of 42-gallon barrels (bbl) of oil collected by the suctioning process. A graphic similar to the one used by BP is shown below. a. Note that the vertical axis represents the “cumulative” number of barrels collected per day. This is calculated by adding the amounts of the previous days’ oil collection to the current day’s oil collection. Explain why this graph is misleading. b. Estimates of the actual number of barrels of oil collected per day for each of the 8 days are listed in the accompanying table. Construct a graph for these data that accurately depicts BP’s progress in its daily collection of oil. What conclusions can you draw from the graph?

Construct a relative frequency histogram for the data summarized in the accompanying table.

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 to a. = 60, = 10 b. = 50, = 5 c. = 40, = 10 d. = 40, = 100

Refer to Exercise 2.141. For parts a - d, determine whether the values 50, 70, and 80 are outliers.

For each of the following data sets, compute , s2, and s: a. 13, 1, 10, 3, 3 b. 13, 6, 6, 0 c. 1, 0, 1, 10, 11, 11, 15 d. 3, 3, 3, 3

For each of the following data sets, compute , s2, and s. If appropriate, specify the units in which your answers are expressed.

Construct a scattergram for the data in the following table.

Blogs for Fortune 500 firms. Web site communication through blogs and forums is a key marketing tool for companies. The Journal of Relationship Marketing (Vol. 7, 2008) investigated the prevalence of blogs and forums at Fortune 500 firms with both English and Chinese Web sites. a. Of the firms that provided blogs/forums as a marketing tool, the accompanying table gives a breakdown on the entity responsible for creating the blogs/forums. Use a graphical method to describe the data summarized in the table. Interpret the graph. b. In a sample of firms that provide blogs and forums as marketing tools, the mean number of blogs/forums per site was 4.25, with a standard deviation of 12.02. Provide an interval that is likely to contain the number of blogs/ forums per site for at least 75% of the Fortune 500 firms in the sample. c. Do you expect the distribution of the number of blogs/ forums to be symmetric, skewed right, or skewed left? Explain.

Management system failures. The U.S. Chemical Safety and Hazard Investigation Board (CSB) is responsible for determining the root cause of industrial accidents (Process Safety Progress, December 2004). The accompanying table gives a breakdown of the root causes of 83 incidents caused by management system failures. a. Find the relative frequency of the number of incidents for each cause category. b. Construct a Pareto diagram for the data. c. From the Pareto diagram, identify the cause categories with the highest (and lowest) relative frequency of incidents.

Business marketing publications. Business-to-business marketing describes the field of marketing between multiple business entities. The Journal of Business-to-Business Marketing (Vol. 15, 2008) produced a pie chart describing the number of business-to-business marketing articles published in all journals, by topical area, between 1971 and 2006. The data used to produce the pie chart are shown in the table. a. Compute the relative frequencies for the nine topical areas shown in the table. Interpret the relative frequency for Buyer Behavior. b. Use the relative frequencies, part a, to construct a pie chart for the data. Why is the slice for Marketing Research smaller than the slice for Sales Management?

U.S. business bankruptcies. The American Bankruptcy Institute and the National Bankruptcy Research Center monitor the number of business bankruptcy filings each quarter. The table below lists the number of business bankruptcy filings for each quarter of a recent 2-year period. FILING a. Explain why the data in the table represent time series data. b. Construct a time series plot for the quarterly number of bankruptcy filings. c. Do you detect a trend in the time series plot? Explain.

Safety Administration (NHTSA) crash-tests new car models to determine how well they protect the driver and front-seat passenger in a head-on collision. The NHTSA has developed a “star” scoring system for the frontal crash test, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the better the level of crash protection in a head-on collision. The NHTSA crash test results for 98 cars (in a recent model year) are stored in the accompanying data file. a. The driver-side star ratings for the 98 cars are summarized in the Minitab printout shown below. Use the information in the printout to form a pie chart. Interpret the graph. b. One quantitative variable recorded by the NHTSA is driver’s severity of head injury (measured on a scale from 0 to 1,500). The mean and standard deviation for the 98 driver head-injury ratings are displayed in the Minitab printout below. Give a practical interpretation of the mean. c. Use the mean and standard deviation to make a statement about where most of the head-injury ratings fall. d. Find the z-score for a driver head-injury rating of 408. Interpret the result.

Defects in new automobiles. Consider the following data from the automobile industry. All cars produced on a particular day were inspected for defects. The 145 defects found were categorized by type as shown in the accompanying table. a. Construct a Pareto diagram for the data. Use the graph to identify the most frequently observed type of defect. b. All 70 car body defects were further classified as to type. The frequencies are provided in the following table. Form a Pareto diagram for type of body defect. (Adding this graph to the original Pareto diagram of part a is called exploding the Pareto diagram.) Interpret the result. What type of body defect should be targeted for special attention?

U.S. wine export markets. The Center for International Trade Development (CITD), provides a listing of the top 30 U.S. export markets for sparkling wines. Data on the amount exported (thousands of dollars) and 3-year percentage change for the 30 countries in a recent year are saved in the WINEX file. (Data for 5 countries are listed in the table.) Descriptive statistics for these variables are shown in the Minitab printout (next column). a. Locate the mean amount exported on the printout and practically interpret its value. b. Locate the median amount exported on the printout and practically interpret its value. c. Locate the mean 3-year percentage change on the printout and practically interpret its value. d. Locate the median 3-year percentage change on the printout and practically interpret its value. e. Use the information on the printout to find the range of the amount exported. f. Locate the standard deviation of the amount exported on the printout. g. Use the result, part f, to find the variance of the amount exported. h. If one of the top 30 countries is selected at random, give an interval that is likely to include the export amount for this country.

Color and clarity of diamonds. Diamonds are categorized according to the “four C’s”: carats, clarity, color, and cut. Each diamond stone that is sold on the open market is provided a certificate by an independent diamond assessor that lists these characteristics. Data for 308 diamonds were extracted from Singapore’s Business Times (Journal of Statistics Education, Vol. 9, No. 1, 2001). Color is classified as D, E, F, G, H, or I, while clarity is classified as IF, VVS1, VVS2, VS1, or VS2. In addition to color and clarity, the independent certification group (GIA, HRD, or IGI), the number of carats and the asking price were recorded. a. Use a graphical technique to summarize the color and clarity of the 308 diamond stones. What is the color and clarity that occurs most often? Least often? b. Use a graphical method to describe the carat distribution of all 308 diamonds. c. Use a graphical method to describe the carat distribution of diamonds certified by the GIA group. d. Repeat part c for the HRD and IGI certification groups. e. Compare the three carat distributions, parts c and d. Is there one particular certification group that appears to be assessing diamonds with higher carats than the others? f. Find and interpret the mean of the data set. g. Find and interpret the median of the data set. h. Find and interpret the mode of the data set. i. Which measure of central tendency best describes the 308 carat values? Explain. j. Use the mean and standard deviation to form an interval that will contain at least 75% of the carat values in the data set. k. Construct a scatterplot for the data, with number of carats on the horizontal axis and price on the vertical axis. What type of trend do you detect?

Time to develop price quotes. 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 potential customers. To remedy this problem, the firm’s management would like to set guidelines for the length of time each department should spend developing price quotes. To help develop these guidelines, 50 requests for price quotes were randomly selected from the set of price quotes made last year: the processing time (in days) was determined for each price quote for each department. Several observations are displayed in the table below. The price quotes are also classified by whether or not they were “lost” (i.e., whether or not the customer placed an order after receiving the price quote). a. Construct a stem-and-leaf display for the total processing time for each department. Shade the leaves that correspond to “lost” orders in each of the displays, and interpret each of the displays. b. Using your results from part a, develop “maximum processing time” guidelines for each department that, if followed, will help the firm reduce the number of lost orders. c. Generate summary statistics for the processing times. Interpret the results. d. Calculate the z-score corresponding to the maximum processing time guideline you developed in part b for each department, and for the total processing time. e. Calculate the maximum processing time corresponding to a z-score of 3 for each of the departments. What percentage of the orders exceed these guidelines? How does this agree with Chebyshev’s Rule and the Empirical Rule? f. Repeat part e using a z-score of 2. g. Compare the percentage of “lost” quotes with corresponding times that exceed at least one of the guidelines in part e to the same percentage using the guidelines in part f. Which set of guidelines would you recommend be adopted? Why?

Doctors and ethics. For physicians confronted with ethical dilemmas (e.g., end-of-life issues or treatment of patients without insurance), many hospitals provide ethics consultation services. However, not all physicians take advantage of these services and some refuse to use ethics consultation. The extent to which doctors refuse ethics consults was studied in the Journal of Medical Ethics (Vol. 32, 2006). Survey questionnaires were administered to all physicians on staff at a large community hospital in Tampa, Florida, and 118 physicians responded. Several qualitative variables were measured, including previous use of ethics consultation (“never used” or “used at least once”), practitioner specialty (“medical” or “surgical”), and future use of ethics consultation (“yes” or “no”). a. Access the file and generate a graph that describes the level to which the physicians on staff have previously used the ethics consultation services. What proportion of the sampled physicians have never used ethics consultation? b. Repeat part a for future use of ethics consultation. What proportion of the sampled physicians state that they will not use the services in the future? c. Generate side-by-side graphs that illustrate differences in previous use of ethics consultation by medical and surgical specialists. What inference can you make from the graphs? d. Repeat part C for future use of ethics consultation. e. One of the quantitative variables measured in the survey of physicians was length of time in practice (i.e., years of experience). The medical researchers hypothesized that older, more experienced physicians would be less likely to use ethics consultation in the future. Generate two graphs to describe the distribution of years of experience—one for physicians who indicated they would use ethics consultation in the future and one for physicians who refused to use ethics consultation. Place the graphs side by side. Is there support for the researchers’ assertion? Explain. f. Find the mean, median, and mode for the length of time in practice (i.e., years of experience) variable. Give a practical interpretation of each of these measures of central tendency. g. Consider only the physicians who would refuse to use ethics consultation in the future. Find the mean, median, and mode for the length of time in practice for these physicians. Practically interpret the results. h. Repeat part g for physicians who would use ethics consultation in the future. i. Use the results, parts g and h, to comment on the medical researchers’ theory. j. Find the range, variance, and standard deviation for the length of time in practice (i.e., years of experience) variable. If possible, give a practical interpretation of each of these measures of variation. k. Consider only the physicians who would refuse to use ethics consultation in the future. Find the standard deviation for the length of time in practice for these physicians. l. Repeat part k for physicians who would use ethics consultation in the future. m. Use the results, parts k and l, to compare the variation in the length of time in practice distributions for physicians who would use and who would refuse ethics consultation in the future. n. In addition to length of time in practice (i.e., years of experience), the researchers also measured the amount of exposure to ethics in medical school (number of hours) for the sample of 118 physicians. Create a scatterplot for these two variables. Plot years of experience on the vertical axis and amount of exposure to ethics in medical school on the horizontal axis. Comment on the strength of the association between these two variables. o. Conduct an outlier analysis of the data for the variable amount of exposure to ethics in medical school. Identify the highly suspect outlier in the data set. p. Remove the outlier, part o, from the data set and re-create the scatterplot of part n. What do you observe?

U.S. peanut production. If not examined carefully, the graphical description of U.S. peanut production shown at the top of the next page can be misleading. a. Explain why the graph may mislead some readers. b. Construct an undistorted graph of U.S. peanut production for the given years.

Age discrimination study. 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 discrimination cases are of two types: disparate treatment and disparate impact. In the former, the issue is whether workers have been intentionally discriminated against. In the latter, the issue is whether employment practices adversely affect the protected class (i.e., workers 40 and over) even though no such effect was intended by the employer. A small computer manufacturer laid off 10 of its 20 software engineers. The ages of all engineers at the time of the layoff are shown below. Analyze the data to determine whether the company may be vulnerable to a disparate impact claim.

No Child Left Behind Act. According to the government, federal spending on K-12 education has increased dramatically over the past 20 years, but student performance has essentially stayed the same. Hence, in 2002, President George Bush signed into law the No Child Left Behind Act, a bill that promised improved student achievement for all U.S. children. Chance (Fall 2003) reported on a graphic obtained from the U.S. Department of Education Web site (www.ed.gov) that was designed to support the new legislation. The graphic is reproduced on the previous page. The bars in the graph represent annual federal spending on education, in billions of dollars (left-side vertical axis). The horizontal line represents the annual average fourth-grade children’s reading ability score (right-side vertical axis). Critically assess the information portrayed in the graph. Does it, in fact, support the government’s position that our children are not making classroom improvements despite federal spending on education? Use the following facts (divulged in the Chance article) to help you frame your answer: (1) The U.S. student population has also increased dramatically over the past 20 years, (2) fourth-grade reading test scores are designed to have an average of 250 with a standard deviation of 50, and (3) the reading test scores of seventh and twelfth graders and the mathematics scores of fourth graders did improve substantially over the past 20 years.

Steel rod quality. In his essay “Making Things Right,” W. Edwards Deming considered the role of statistics in the quality control of industrial products.* In one example, Deming examined the quality-control process for a manufacturer of steel rods. Rods produced with diameters smaller than 1 centimeter fit too loosely in their bearings and ultimately must be rejected (thrown out). To determine whether the diameter setting of the machine that produces the rods is correct, 500 rods are selected from the day’s production and their diameters are recorded. The distribution of the 500 diameters for one day’s production is shown in the accompanying figure. Note that the symbol LSL in the figure represents the 1-centimeter lower specification limit of the steel rod diameters. There has been speculation that some of the inspectors are unaware of the trouble that an undersized rod diameter would cause later in the manufacturing process. Consequently, these inspectors may be passing rods with diameters that are barely below the lower specification limit and recording them in the interval centered at 1.000 centimeter. According to the figure, is there any evidence to support this claim? Explain.

Discuss the conditions under which the median is preferred to the mean as a measure of central tendency.

Explain why we generally prefer the standard deviation to the range as a measure of variability for quantitative data.

If the range of a set of data is 20, find a rough approximation to the standard deviation of the data set.

Motivation of drug dealers. Refer to the Applied Psychology in Criminal Justice (September 2009) study of convicted drug dealers’ motivations, Exercise 2.80 (p. 87). Recall that the sample of drug dealers had a mean Wanting Recognition (WR) score of 39 points, with a standard deviation of 6 points. a. Find and interpret the z-score for a drug dealer with a WR score of 30 points. b. What proportion of the sampled drug dealers had WR scores below 39 points? (Assume the distribution of WR scores is mound-shaped and symmetric.) c. If 5% of convicted drug dealers have WR scores above 49 points, give a percentile ranking for the WR score of 49.

Products “Made in the USA.” “Made in the USA” is a claim stated in many product advertisements or on product labels. Advertisers want consumers to believe that the product is manufactured with 100% U.S. labor and materials—which is often not the case. What does “Made in the USA” mean to the typical consumer? To answer this question, a group of marketing professors conducted an experiment at a shopping mall (Journal of Global Business, Spring 2002). They asked every fourth adult entrant to the mall to participate in the study. A total of 106 shoppers agreed to answer the question, “‘Made in the USA’ means what percentage of U.S. labor and materials?” The responses of the 106 shoppers are summarized as follows: “100%” (64 shoppers), “75 to 99%” (20 shoppers), “50 to 74%” (18 shoppers), and “less than 50%” (4 shoppers). a. What type of data-collection method was used? b. What type of variable, quantitative or qualitative, is measured? c. Present the data in graphical form. Use the graph to make a statement about the percentage of consumers who believe “Made in the USA” means 100% U.S. labor and materials.

Drivers stopped by police. According to the Bureau of Justice Statistics (September 2013), 80% of all licensed drivers stopped by police are 25 years or older. Give a percentile ranking for the age of 25 years in the distribution of all ages of licensed drivers stopped by police.

Hull failures of oil tankers. Owing to several major ocean oil spills by tank vessels, Congress passed the Oil Pollution Act, which requires all tankers to be designed with thicker hulls. Further improvements in the structural design of a tank vessel have been proposed since then, each with the objective of reducing the likelihood of an oil spill and decreasing the amount of outflow in the event of a hull puncture. To aid in this development, Marine Technology (Jan. 1995) reported on the spillage amount (in thousands of metric tons) and cause of puncture for 42 major oil spills from tankers and carriers. [Note: Cause of puncture is classified as either collision (C), fire/explosion (FE), hull failure (HF), or grounding (G).] The data are saved in the accompanying file. a. Use a graphical method to describe the cause of oil spillage for the 42 tankers. Does the graph suggest that any one cause is more likely to occur than any other? How is this information of value to the design engineers? b. Find and interpret descriptive statistics for the 42 spillage amounts. Use this information to form an interval that can be used to predict the spillage amount of the next major oil spill.

Software defects. The Promise Software Engineering Repository is a collection of data sets available to serve businesses in building predictive software models. One such data set, saved in the accompanying file, contains information on 498 modules of software code. Each module was analyzed for defects and classified as “true” if it contained defective code and “false” if not. Access the data file and produce a bar graph or a pie chart for the defect variable. Use the graph to make a statement about the likelihood of defective software code.

Velocity of Winchester bullets. The American Rifleman (June 1993) reported on the velocity of ammunition fired from the FEG P9R pistol, a 9 mm gun manufactured in Hungary. Field tests revealed that Winchester bullets fired from the pistol had a mean velocity (at 15 feet) of 936 feet per second and a standard deviation of 10 feet per second. Tests were also conducted with Uzi and Black Hills ammunition. a. Describe the velocity distribution of Winchester bullets fired from the FEG P9R pistol. b. A bullet, brand unknown, is fired from the FEG P9R pistol. Suppose the velocity (at 15 feet) of the bullet is 1,000 feet per second. Is the bullet likely to be manufactured by Winchester? Explain.

Trend in Iraq War casualties. While the United States was still actively fighting in the Iraq War, a news media outlet produced a graphic showing a dramatic decline in the annual number of American casualties. The number of deaths for the years 2003, 2004, 2005, and 2006 were (approximately) 475, 850, 820, and 130, respectively. a. Create a time series plot showing the dramatic decline in the number of American deaths per year. b. The graphic was based on data collected through February of 2006. Knowing this fact, why is the time series plot misleading? c. What information would you like to have in order to construct a graph that accurately reflects the trend in American casualties from the Iraq War?

History of corporate acquisitions. Refer to the Academy of Management Journal (Aug. 2008) study of corporate acquisitions from 1980 to 2000, Exercise 2.12 (p. 50). a. Construct a time series plot of the number of firms with at least one acquisition. b. For each year, compute the percentage of sampled firms with at least one acquisition. Then construct a time series plot of these percentages. c. Which time series plot, part a or part b, is more informative about the history of corporate acquisitions over time? Explain.

Radiation levels in homes. In some locations, radiation levels in homes are measured at well above normal background levels in the environment. As a result, many architects and builders are making design changes to ensure adequate air exchange so that radiation will not be “trapped” in homes. In one such location, 50 homes’ levels were measured, and the mean level was 10 parts per billion (ppb), the median was 8 ppb, and the standard deviation was 3 ppb. Background levels in this location are at about 4 ppb. a. Based on these results, is the distribution of the 50 homes’ radiation levels symmetric, skewed to the left, or skewed to the right? Why? b. Use both Chebyshev’s Rule and the Empirical Rule to describe the distribution of radiation levels. Which do you think is most appropriate in this case? Why? c. Use the results from part b to approximate the number of homes in this sample that have radiation levels above the background level. d. Suppose another home is measured at a location 10 miles from the one sampled and has a level of 20 ppb. What is the z-score for this measurement relative to the 50 homes sampled in the other location? Is it likely that this new measurement comes from the same distribution of radiation levels as the other 50? Why? How would you go about confirming your conclusion?

Investigating the claims of weight-loss clinics. The U.S. Federal Trade Commission assesses fines and other penalties against weight-loss clinics that make unsupported or misleading claims about the effectiveness of their programs. Brochures from two weight-loss clinics both advertise “statistical evidence” about the effectiveness of their programs. Clinic A claims that the mean weight loss during the first month is 15 pounds; Clinic B claims a median weight loss of 10 pounds. a. Assuming the statistics are accurately calculated, which clinic would you recommend if you had no other information? Why? b. Upon further research, the median and standard deviation for Clinic A are found to be 10 pounds and 20 pounds, respectively, while the mean and standard deviation for Clinic B are found to be 10 and 5 pounds, respectively. Both are based on samples of more than 100 clients. Describe the two clinics’ weight-loss distributions as completely as possible given this additional information. What would you recommend to a prospective client now? Why? c. Note that nothing has been said about how the sample of clients upon which the statistics are based was selected. What additional information would be important regarding the sampling techniques employed by the clinics?