The Practice Of Statistics For Business And Economics 3rd Edition David S. Moore, George P. McCabe, Layth C. Alwan, Bruce A. Craig, William M. Duckworth - Solutions

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Is it reallyPoisson? Certain manufacturing environments, such as semiconductor manufacturing and biotechnology, require a low level of environmental pollutants (for example, dust, airborne microbes, and aerosol particles). For such industries, manufacturing occurs in ultraclean environments known
Monitoring budgets. Control charts are used for a wide variety of applications in business. In the accounting area, control charts can be used to monitor budget variances. A budget variance is the difference between planned spending and actual spending for a given time period. Often budget
Monitoring rare events. In certain SPC applications, we are concerned with monitoring the occurrence of events that can occur at any point within a continuous interval of time, such as the number of computer operator errors per day or plant injuries per month. However, for highly capable processes,
It’s all in the wrist. Consider the saga of a professional basketball player plagued with poor free-throw shooting performance.Below are the number of free throws he made out of 50 attempts on 20 consecutive practice days: DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Even more signals. There are other out-of-control signals that are sometimes used with x charts. One is “15 points in a row within the 1σ level.” That is, 15 consecutive points fall between μ − σ/√n and μ + σ/√n. This signal suggests either that the value of σ used for the chart is
Bone density revisited. Refer to Exercise 12.26 (page 666), in which you were asked to construct x and R charts for the calibration data from a Lunar bone densitometer shown in Table 12.6. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Hospital losses revisited. Refer to Exercise 12.14 (page 654), in which you were asked to construct x and s charts for the hospital losses data shown in Table 12.4. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Categorizing the output. Previously, control of the process was based on categorizing the thickness of each film inspected as satisfactory or not. Steady improvement in process quality has occurred, so that just 15 of the last 5000 films inspected were unsatisfactory.(a) What type of control chart
x chart. Interviews with the operators reveal that in Samples 1 and 10 mistakes in operating the interferometer resulted in one high-outlier thickness reading that was clearly incorrect.Recalculate s after removing Samples 1 and 10. Recalculate UCL for the s chart and add the new UCL to your s
s chart. Calculate control limits for s, make an s chart, and comment on control of short-term process variation.
Purchased material. At the present time, about 5 lots out of every 1000 lots of material arriving at a plant site from outside vendors are rejected because they are incorrect. The plant receives about 300 lots per week. As part of an effort to reduce errors in the system of placing and filling
Pareto charts. You manage the customer service operation for a maker of electronic equipment sold to business customers.Traditionally, the most common complaint is that equipment does not operate properly when installed, but attention to manufacturing and installation quality will reduce these
Enlighten management.Amanagerwhoknows no statistics asks you, “What does it mean to say that a process is in control? Is being in control a guarantee that the quality of the product is good?” Answer these questions in plain language that the manager can understand.
Implications of out-of-control signal. For attribute control charts, explain the difference in implications for a process and in actions to be taken when the plotted statistic falls beyond the upper control limit versus beyond the lower control limit.
Purchase order errors. Purchase orders are checked for two primary mistakes: incorrect charge account number and missing required information. Each day, 10 purchase orders are randomly selected, and the number of mistakes in the sample is recorded. Here are the numbers of mistakes observed for 20
Monitoring lead time demand. Refer to the lead time demand process discussed in Exercise 5.129 (page 329). Assuming the Poisson distribution given in the exercise, what would be the appropriate control chart limits for monitoring lead time demand?
p charts and high-quality processes. A manufacturer of consumer electronic equipment makes full use not only of statistical process control but of automated testing equipment that efficiently tests all completed products. Data from the testing equipment show that finished products have only 3.5
School absenteeism. Here are data from an urban school district on the number of eighth-grade students with three or more unexcused absences from school during each month of a school year. Because the total number of eighth-graders changes a bit from month to month, these totals are also given for
Call center. A large nationwide retail chain keeps track of a variety of statistics on its service call center. One of those statistics is the length of time a customer has to wait before talking to a representative. Based on call center research and general experience, the retail chain has
Aircraft rivets. After completion of an aircraft wing assembly, inspectors count the number of missing or deformed rivets.There are hundreds of rivets in each wing, but the total number varies depending on the aircraft type. Recent data for wings with a total of 34,700 rivets show 208 missing or
Positive lower control limit? What values of c are associated with a positive lower control limit for the c chart?
Worker safety. Aninvestigation of the out-of-control signal seen in Figure 12.20 revealed that not only were there newhires that month but newmachinerywas installed.The combination of relatively inexperienced employees and unfamiliarity with the new machinery resulted in an unusually high number of
Setting up a p chart. After inspecting Figure 12.18 (page 672), you decide to monitor the future absenteeism rates using a center line and control limits calculated from the second two weeks of data recorded in Table 12.8. Find p for these 10 days and give the new values of CL, LCL, and UCL.
Unpaid invoices. The controller’s office of a corporation is concerned that invoices that remain unpaid after 30 days are damaging relations with vendors. To assess the magnitude of the problem, a manager searches payment records for invoices that arrived in the past 10 months. The average number
More on six-sigma quality (optional). The originators of the “six-sigma quality” standard reasoned as follows. Shortterm process variation is described by σ. In the long term, the process mean μ will also vary. Studies show that in most manufacturing processes, ±1.5σ is adequate to allow
Six-sigma quality (optional). A process with Cp ≥ 2 is sometimes said to have “six-sigma quality.” Sketch the specification limits and a Normal distribution of individual measurements for such a process when it is properly centered. Explain from your sketch why this is called six-sigma
Alloy composition process capability (optional). Obtain the individual observations from the 20 preliminary subgroups studied in Exercise 12.28. The acceptable range for the percent of aluminum is 3.8% to 4.2%.(a) Make a Normal quantile plot of the 60 observations. What do you conclude? (If your
Measuring your personal capability (optional). Refer to Exercise 12.33, in which you collected 50 sequential observations on your ability to measure 5 seconds. Suppose we define acceptable performance as 5 ± 0.15 seconds.(a) Assume that the Normal distribution is sufficiently adequate to describe
Hospital losses again (optional). Table 12.4 (page 655)gives data on a hospital’s losses for 120 joint replacement patients, collected as 15 monthly samples of 8 patients each. The process has been in control and losses have a roughly Normal distribution. The sample standard deviation (s) for the
Measuring capability (optional). You are in charge of a process that makes metal clips. The critical dimension is the opening of a clip, which has specifications 15 ± 0.5 millimeters(mm). The process is monitored by x and s charts based on samples of 5 consecutive clips each hour. Control has
Estimating nonconformance rate. Suppose a Normally distributed process is centered on target with the target being halfway between specification limits. If ˆC p = 0.80, what is the estimated rate of nonconformance of the process to the specifications?
Control charting your reaction times. Consider the following personal data-generating experiment. Obtain a stopwatch, a capability that many electronic watches offer. Alternatively, you can use one of many Web-based stopwatches easily found with a Google search (make sure to use a site that reports
Financial market movements. Financial reporters and investors often perceive movements in individual stock prices, mutual funds, and market indices as unusual. Consider the weekto-week changes in the S&P 500 market index from April 6, 2009, to December 28, 2009.(a) Construct a histogram of market
Accounts receivable. In an attempt to understand the bill-paying behavior of its distributors, a manufacturer samples bills and records the number of days between the issuing of the bill and the receipt of payment. The manufacturer formed subgroups of 10 randomly chosen bills per week over the
Deming speaks. The quality guru W. Edwards Deming(1900–1993) taught (among much else) that(a) “Peoplework in the system. Management creates the system.”(b) “Putting out fires is not improvement. Finding a point out of control, finding the special cause and removing it, is only putting the
Alloy composition—prospective control. Project the x and R chart limits found in the previous exercise for prospective control of aluminum content. The last 15 rows of Table 12.7 give data on the next 15 future subgroups. Refer to Exercise 12.27 and apply the nine-in-a-row rule along with the
Alloy composition—retrospective control. Die casts are used to make molds for molten metal to produce a wide variety of products ranging from kitchen and bathroom fittings to toys, doorknobs, and a variety of auto and electronic components. Die casts themselves are made out of an alloy of metals
Additional out-of-control signals. A single extreme point outside three-sigma limits represents one possible statistical signal of unusual process behavior. As we saw in the Kobe Bryant application (Example 12.5, page 656), special causes can also give rise to unusual variation within control
Measuring bone density. Loss of bone density is a serious health problem for many people, especially older women.Conventional X-rays often fail to detect loss of bone density until the loss reaches 25% or more. New equipment such as the Lunar bone densitometer is much more sensitive.Ahealth clinic
Monitoring packaged products. To control the fill amount of its cereal products, a cereal manufacturer monitors the net weight of the product with x and R charts using a subgroup size of n = 5. One of its brands, Organic Bran Squares, has a target of 10.6 ounces. Suppose that 20 preliminary
Alternative control limits. American and Japanese practice uses three-sigma control charts. That is, the control limits are 3 standard deviations on either side of the mean. When the statistic being plotted has a Normal distribution, the probability of a point outside the limits is about 0.003 (or
Probability out? An x chart plots the means of samples of size 4 against center line CL = 700 and control limits LCL =687 and UCL = 713. The process has been in control. Now the process is disrupted in a way that changes the mean to μ = 693 and the standard deviation to σ = 12. What is the
Dyeing yarn. The unique colors of the cashmere sweaters your firm makes result from heating undyed yarn in a kettle with a dye liquor. The pH (acidity) of the liquor is critical for regulating dye uptake and hence the final color. There are 5 kettles, all of which receive dye liquor from a common
O-ring capability in terms of percent defective. Refer to Example 12.9 for the mean and standard deviation estimates for the O-ring application.Using software, estimate the percent of O-rings that do not meet specs. In quality applications, it is common to report defective rates in units of parts
Cp versus Cpk. Sketch Normal curves that represent measurements on products from a process with(a) Cp = 3 and Cpk = 1.(b) Cp = 3 and Cpk = 2.(c) Cp = 3 and Cpk = 3.
Specification limits versus control limits. The manager you report to is confused by LSL and USL versus LCL and UCL. The notations look similar. Carefully explain the conceptual difference between specification limits for individual measurements and control limits for x.
Kobe Bryant in the playoffs. The control charts of Example 12.5 and Exercise 12.16 are based on the regular-season performance. After the conclusion of the regular season, Kobe Bryant’s team (LA Lakers) played in the playoffs. Below are his points per minute in the playoffs (read left to
Personal processes. From your personal life, provide two examples of processes for which you would collect data in the form of individual measurements that ultimately might be monitored by an I chart.
Kobe Bryant. In Example 12.5, we observed two unusual observations associated with an injury to Kobe Bryant. Remove these two points and reestimate the center line and control limits. Comment on the process relative to the revised limits.
Lab testing. Show the computations that confirm the limits of the x chart and s chart shown in Figure 12.10.
Hospital losses. Both nonprofit and for-profit hospitals are financially pressed by restrictions on reimbursement by insurers and the government. One hospital looked at their losses broken down by diagnosis. The leading source was joint replacement surgery. Table 12.4 gives data on the losses (in
O-rings. Show the computations that confirm the limits of the x chart and R chart shown in Figure 12.9.
Auto thermostats. A maker of auto air conditioners checks a sample of 4 thermostatic controls from each hour’s production. The thermostats are set at 75◦F and then placed in a chamber where the temperature is raised gradually. The temperature at which the thermostat turns on the air conditioner
Interpreting signals. Explain the difference in the interpretation of a point falling beyond the upper control limit of the x chart versus a point falling beyond the upper control limit of the R chart.
Pareto charts. Painting new auto bodies is a multistep process. There is an “electrocoat” that resists corrosion, a primer, a color coat, and a gloss coat. A quality study for one paint shop produced this breakdown of the primary problem type for those autos whose paint did not meet the
Pareto charts. Continue the study in the previous two exercises of the process of getting to work or class on time. If you kept good records, you could make a Pareto chart of the reasons(special causes) for late arrivals at work or class. Make a Pareto chart that you think roughly describes your
Common cause, special cause. Each weekday morning, you must get to work or to your first class on time. The time at which you reach work or class varies from day to day, and your planning must allow for this variation. List several common causes of variation in your arrival time. Then list several
Describe a process. Each weekday morning, you must get to work or to your first class on time. Make a flowchart of your daily process for doing this, starting when you wake. Be sure to include the time at which you plan to start each step.
Which type of control chart? For each of the following process outcomes indicate if a variable control chart or an attribute control chart is most applicable:(a) Number of lost-baggage claims per day.(b) Time to respond to a field service call.(c) Thickness (in millimeters) of cold-rolled steel
Commoncauses and special causes. In Exercise 12.1, you described the process of getting on an airplane. What are some sources of common cause variation in this process? What are some special causes that can result in out-of-control variation?
Special causes. Jeannine participates in bicycle road races. She regularly rides 25 kilometers over the same course in training. Her time varies a bit from day to day but is generally stable. Give several examples of special causes that might raise or lower Jeannine’s time on a particular day.
Causes of variation. Consider the process of uploading a photo to a Facebook account. Brainstorm at least five possible causes for variation in upload time. Construct a cause-and-effect diagram based on your identified potential causes.
Operational definition and measurement. If asked to measure the percent of late departures of an airline, you are faced with an unclear task. Is late departure defined in terms of “leaving the gate” or “taking off from the runway”? What is required is an operational definition of the
Describe a process. Consider the process of going from curbside to sitting in your assigned airplane seat. Make a flowchart of the process. Do not forget to consider steps that involve Yes/No outcomes.
The effect of gender. In the previous two exercises, you analyzed the males and females using separate multiple regressions with the high school grades as explanatory variables. Here we will run the analyses together. Recode the variable Sex into a new variable Gender that is an indicator variable.
Analyze the females and compare. Refer to the previous exercise. Perform the analysis using the data for females only. Are there any important differences between female and male students in predicting GPA?
Analyze the males. The variable Sex has the value 1 for males and 2 for females. Create a data set containing the values for males only. Run a multiple regression analysis for predicting GPAfrom the three high school grade variables for this group. Interpret the results and state what conclusions
Use the verbal explanatory variables. How well do verbal variables predict the performance of computer science students? Perform a multiple regression analysis to predict GPA from HSE and SATV. Summarize the results and compare them with those obtained in the previous exercise. In what ways do the
Use the math explanatory variables. It appears that the mathematics explanatory variables are strong predictors of GPA for computer science students. Run a multiple regression using HSM and SATM to predict GPA.(a) Give the fitted regression equation.(b) State the H0 and Ha tested by the ANOVA F
Predict GPA from SAT scores. Use the two SAT scores in a multiple regression to predict GPA. Calculate and store the residuals. Plot the residuals versus each of the explanatory variables and versus the predicted GPA. Describe the plots.
Predict GPA from high school grades. Regress GPA on the three high school grade variables. Calculate and store the residuals from this regression. Plot the residuals versus each of the three predictors and versus the predicted value of GPA. Are there any unusual points or patterns in these four
High school grades and GPA. Make a plot of GPA versus HSM. Do the same for the other two high school grade variables. Describe the three plots. Are there any outliers or influential points?
SAT scores and GPA. Use software to make a plot of GPAversus SATM. Do the same for GPAversus SATV. Describe the general patterns. Are there any unusual values?
Predict the yield for another year. Repeat the previous exercise doing the prediction for 2020. Compare the results of this exercise with the previous one. Also explain why the predicted values are beginning to differ more substentially.
Do a prediction. Use the simple linear regression model with corn yield as the response variable and year as the explanatory variable to predict the corn yield for the year 2008, and give the 95% prediction interval. Also, use the multiple regression model where year and year2 are both explanatory
Compare models. Run the model to predict corn yield using year and the squared term year2 defined in the previous exercise.(a) Summarize the significance test results.(b) The coefficient for year2 is not statistically significant in this run, but it was significant in the model analyzed in the
Try a quadratic. We need a new variable to model the curved relation that we see between corn yield and year in the residual plot of the last exercise. Let year2 = (year − 1982)2.(When adding a squared term to a multiple regression model, we sometimes subtract the mean of the variable being
Use both predictors. From the previous two exercises, we conclude that year and soybean yield may be useful together in a model for predicting corn yield. Run this multiple regression.(a) Explain the results of the ANOVA F test. Give the null and alternative hypotheses, the test statistic with
Can soybean yield predict corn yield? Run the simple linear regression using soybean yield to predict corn yield.(a) Summarize the results of your analysis, including the significance test results for the slope and R2 for this model.(b) Analyze the residuals with a Normal quantile plot. Is there
Corn yield varies over time. Run the simple linear regression using year to predict corn yield.(a) Summarize the results of your analysis, including the significance test results for the slope and R2 for this model.(b) Analyze the residuals with a Normal quantile plot. Is there any indication in
Try logs. Because distributions of variables such as PCB and the PCB congeners tend to be skewed, researchers frequently analyze the logarithms of the measured variables. Create a data set that has the logs of each of the variables in the PCB data set. Note that zero is a possible value for PCB126;
Run a new model and compare the results. Run a regression to predict PCB using the variables PCB52, PCB118, and PCB138. Note that this is similar to the analysis that you did in Exercise 11.101 with the change that PCB180 is not included as an explanatory variable.(a) Summarize the results.(b) In
Predicting the total PCB level in fish. Polychlorinated biphenyls (PCBs) are synthetic compounds, called congeners, that are particularly toxic to fetuses and young children. Although PCBs are no longer produced in the United States, they are still found in the environment. Since human exposure to
Price-fixing litigation. Multiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin, the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple
The multiple regression results do not tell the whole story. We use a constructed data set in this problem to illustrate this point. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA
Correlations may not be a good way to screen for multiple regression predictors. We use a constructed data set in this problem to illustrate this point. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA
Impact of word of mouth. Word of mouth (WOM) is informal advice passed between consumers that may have a quick and powerful influence on consumer behavior. Word of mouth may be positive (PWOM), encouraging choice of a certain brand, or negative (NWOM), discouraging that choice. A study investigated
More complicated analyses. Refer to the previous exercise.Investigate the possibility that quadratic terms and interactions would improve the estimation of IBI. Write a summary of your results.
Predicting water quality. Pollution of water resources is a serious problem that can require substantial efforts to improve.To determine the financial resources required, an accurate assessment of the extent of the problem is necessary. The index of biotic integrity (IBI) is a measure of the water
Can we generalize the results? The subjects in this experiment were college students at a large Midwest university who were enrolled in an introductory management course. They received the information about the promotions during a 10-week period during their course. Do you think that these facts
Residuals and other models. Refer to the previous exercise.Analyze the residuals from your analysis and investigate the possibility of using quadratic and interaction terms as predictors.Write a report recommending a final model for this problem with a justification for your recommendation.
Run the multiple regression. Refer to the previous exercise.Run a multiple regression using promotions and discount to predict expected price. Write a summary of your results.
Discount promotions at a supermarket. How does the frequency that a supermarket product is promoted at a discount affect the price that customers expect to pay for the product?Does the percent reduction also affect this expectation? These questions were examined by researchers in a study that used
Business to business (B2B) marketing. A group of researchers were interested in determining the likelihood that a business currently purchasing office supplies via a catalog would switch to purchasing from theWeb site of the same supplier. To do this, they performed an online survey using the
Compare regression coefficients. Again refer to Exercise 11.87. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA DATADATADATADATADATA DATA FILE LOC1(a) In Example 10.5 (page 533),
Examine the assumptions. Refer to the previous exercise.We now ask whether the data meet the requirements of the multiple regression model.(a) Find the residuals and examine their distribution. Summarize what you find.(b) Plot the residuals versus each of the explanatory variables.Describe the
Job stress. Recall Case 10.1 (page 528)which looked at the relationship between perceived job stress and a person’s locus of control (LOC). In addition to the accountant’s locus of control, the person’s age and gender were also obtained.DATADATA DATADATADATA DATADATADATADATADATA
Alternatemovie revenue model. Refer to the data set on movie revenue in Case 11.2 (page 591). The variables Budget, Opening, andUSRevenue all have distributions with long tails. For this problem, let’s consider building a model using the logarithm transformation of these variables. DATADATA
Effect of outliers? In Exercise 11.49 (page 603), we identified two movies that have much higher revenue than predicted. Remove these two movies and repeat the previous exercise. Does the removal of these two movies change which model you prefer?
Predicting movie revenue: model selection.Refer to the data set on movie revenue in Case 11.2 (page 591). In addition to the movie’s budget, opening-weekend revenue, and opening-weekend theater count, the data set also includes a column named Sequel. Sequel is 1 if the corresponding movie is a

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The Practice Of Statistics For Business And Economics 3rd Edition David S. Moore, George P. McCabe, Layth C. Alwan, Bruce A. Craig, William M. Duckworth - Solutions

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