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The Practice Of Statistics For Business And Economics 4th Edition Layth C. Alwan, Bruce A. Craig - Solutions

Measuring your personal capability. 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 6 0.15 seconds.(a) Assume that the Normal distribution is sufficiently adequate to describe your
Hospital losses again. Table 12.4 (page 615)gives data on a hospital’s losses for 120 joint replacement patients, collected as 15 monthly samples of eight patients each. The process has been in control, and losses have a roughly Normal distribution. The sample standard deviation (s) for the
Measuring capability. You are in charge of a process that makes metal clips. The critical dimension is the opening of a clip, which has specifications 15 6 0.5 millimeters (mm). The process is monitored by x and R charts based on samples of five consecutive clips each hour. Control has recently
Estimating nonconformance rate. Suppose a Normally distributed process is centered on target with the target being halfway between specification limits. If C ⁄p 5 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
Patient monitoring. There is an increasing interest in the use of control charts in health care.Many physicians are directly involving patients in proactive monitoring of health measurements such as blood pressure, glucose, and expiratory flow rate.Patients are asked to record measurements for a
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) “People work 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 of three-sigma limits represents one possible statistical signal of unusual process behavior. As we saw with Figure 12.5(a) (page 608), process change can also give rise to unusual variation within control limits.A variety of
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. A health
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 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 three 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
Probability out? An x chart plots the means of samples of size 4 against center line CL 5 700 and control limits LCL 5 687 and UCL 5 713. The process has been in control. Now the process is disrupted in a way that changes the mean to 5 693 and the standard deviation to 5 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 five kettles, all of which receive dye liquor from a
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 5 3 and Cpk 5 1.(b) Cp 5 3 and Cpk 5 2.(c) Cp 5 3 and Cpk 5 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.
LeBron in the playoffs. The control charts of Example 12.5 and Exercise 12.16 are based on regular-season performance. After the conclusion of the regular season, LeBron played in 20 playoff games. Here are his points per minute in the playoffs (read left to right):0.70069 0.80335 0.83372 0.72261
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.
LeBron. In Example 12.5 (pages 616–617), we observed an unusual observation associated with a record-breaking performance. Remove this point and reestimate the center lines and control limits for both the I chart and MR chart. 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 its 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 four thermostatic controls from each hour’s production. The thermostats are set at 758F 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 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 own reasons for lateness. That
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
Common causes and special causes. In Exercise 12.1 (page 597), 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. Rachel 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 Rachel’s time on a particular day.
Causes of variation. Consider the process of uploading a video to an Instagram account from a cell phone. Brainstorm as 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 at an airport to sitting in your assigned airplane seat. Make a flowchart of the process.Do not forget to consider steps that involve Yes/No outcomes.
Prices of homes. Consider the data set used for Case 11.3 (page 566). This data set includes information for several other zip codes. Pick a different zip code and analyze the data. Compare your results with what we found for zip code 47904 in Section 11.3.
Predicting CO2 emissions. The data set CO2MPG contains an SRS of 200 passenger vehicles sold in Canada in 2014. There appears to be a quadratic relationship between CO2 emissions and mile per gallon highway(MPGHWY). CO2MPG(a) Create two new centered variables MPG =MPGHWY-35 and MPG2 = MPG × MPG
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 regression
Predicting U.S. movie revenue. Refer to Case 11.2 (page 550). The data set MOVIES contains several other explanatory variables that are available at the time of release that we did not consider in the examples and exercises. These include• Hype: A numeric value that describes the interest in the
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 substantially. CROPS
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 2014, 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. CROPS(a) Summarize the significance test results.(b) The coefficient for year2 is not statistically significant in this run, but it was highly significant in the model
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 5 s year 2 1985d2. (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. CROPS(a) Explain the results of the ANOVA F test. Give the null and alternative hypotheses, the test statistic
Can soybean yield predict corn yield? Run the simple linear regression using soybean yield to predict corn yield. CROPS(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
Corn yield varies over time. Run the simple linear regression using year to predict corn yield. CROPS(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
The multiple regression results do not tell the whole story. We use a constructed data set in this problem to illustrate this point. DSETB(a) Run the multiple regression using X1 and X2 to predict Y. The F test and the significance tests for the coefficients of the explanatory variables fail to
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. DSETA(a) Find the correlations between the response variable Y and each of the explanatory variables X1 and X2. Plot the data and run the two
Impact of word of mouth. Word of mouth(WOM) is informal advice passed among 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 the
Are separate analyses needed? Refer to the previous exercise. Suppose you wanted to generate a similar table but have it based on results from only one multiple regression rather than on three.(a) Describe what additional explanatory variables you would need to include in your regression model and
Determinants of innovation capability. A study of 367 Australian small/medium enterprise(SME) firms looked at the relationship between perceived innovation marketing capability and two marketing support capabilities, market orientation and management capability. All three variables were measured on
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. PPROMO
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. PPROMO
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 the website of the same supplier. To do this, they performed an online survey using the
Compare regression coefficients. Again refer to Exercise 11.85. ENTRE1(a) In Example 10.5 (page 497), parameter estimates for the model that included just EDUC were obtained.Compare those parameter estimates with the ones obtained from the full model that also includes age and locus of control.
Education and income, continued. Refer to the previous exercise.Provided the data meet the requirements of the multiple regression model, we can now perform inference. ENTRE1(a) Test the hypothesis that the coefficients for education, locus of control, and age are all zero. Give the test statistic
Education and income. Recall Case 10.1 (pages 485–486), which looked at the relationship between an entrepreneur’s log income and level of education. In addition to the level of education, the entrepreneur’s age and a measure of his or her perceived control of the environment (locus of
Alternate movie revenue model. Refer to the data set on movie revenue in Case 11.2 (page 550). The variables Budget, Opening, and USRevenue all have distributions with long tails.For this problem, let’s consider building a model using the logarithm transformation of these variables. MOVIES(a) Run
Effect of an outlier. In Exercise 11.50 (page 563), we identified a movie that had much higher revenue than predicted. Remove this movie and repeat the previous exercise. Does the removal of this movie change which model you prefer?
Predicting movie revenue: Model selection. Refer to the data set on movie revenue in Case 11.2 (page 550). In addition to the movie’s budget, opening-weekend revenue, and openingweekend theater count, the data set also includes a column named Sequel. Sequel is 1 if the corresponding movie is a
Predicting movie revenue, continued. Refer to Exercise 11.79. Although a quadratic relationship between total U.S. revenue and theater count provides a better fit than the linear model, it does not make sense that box office revenue would again increase for very low budgeted movies (unless you are
Assessing collinearity in the movie revenue model. Many software packages will calculate VIF values for each explanatory variable.In this exercise, calculate the VIF values using several multiple regressions, and then use them to see if there is collinearity among the movie explanatory variables.
Predicting movie revenue. A plot of theater count versus box office revenue suggests that the relationship may be slightly curved. MOVIES(a) Examine this question by running a regression to predict the box office revenue using the theater count and the square of the theater count. Report the
Write the model. For each of the following situations write a model for y of the formy 5 0 1 1x1 1 2x2 1 Á 1 pxp where p is the number of explanatory variables. Be sure to give the value of p and, if necessary, explain how each of the x’s is coded.(a) A model where the explanatory variable
Differences in slopes and intercepts. Refer to the previous exercise. Verify that the coefficient of x1x2 is equal to the slope for Group B minus the slope for Group A in each of these cases. Also, verify that the coefficient of x1 is equal to the intercept for Group B minus the intercept for Group
Models with interactions. Suppose that x1 is an indicator variable with the value 0 for Group A and 1 for Group B, and x2 is a quantitative variable.Each of the following models describes a relationship between y and the explanatory variables x1 and x2. For each model, substitute the value 0 for
Differences in means. Verify that the coefficient of x in each part of the previous exercise is equal to the mean for Group B minus the mean for Group A. Do you think that this will be true in general?Explain your answer.
Models with indicator variables. Suppose that x is an indicator variable with the value 0 for Group A and 1 for Group B. The following equations describe relationships between the value of y and membership in Group A or B. For each equation, give the value of the mean response y for Group A and
Quadratic models. Sketch each of the following quadratic equations for values of x between 0 and 5. Then describe the relationship between y and x in your own words.(a) y 5 6 1 3x 1 x2.(b) y 5 6 2 3x 1 x2.(c) y 5 6 1 3x 2 x2.(d) y 5 6 2 3x 2 x2.
Residuals. Once we have chosen a model, we must examine the residuals for violations of the conditions of the multiple regression model.Examine the residuals from the model in Example 11.26.(a) Plot the residuals against SqFt. Do the residuals show a random scatter, or is there some systematic
How about the smaller homes? Would it make sense to do the same calculations as in the previous two exercises for homes that have 700 ft2?Explain why or why not.
Suppose the homes are larger. Consider two additional homes, both with 2500 ft2, one with an extra half bath and one without. Find the predicted prices and the difference. How does this difference compare with the difference you obtained in the previous exercise? Explain what you have found.
Comparing some predicted values. Consider two homes, both with 2000 ft2. Suppose the first has an extra half bath and the second does not. Find the predicted price for each home and then find the difference.
The home with three garages. There is only one home with three garage spaces. We might either place this house in the Garage 5 2 group or remove it as unusual. Either decision leaves Garage with values 0, 1, and 2. Based on your plot in the previous exercise, which choice do you recommend?
What about garages? We have not yet examined the number of garage spaces as a possible explanatory variable for price. Make a scatterplot of price versus garage spaces. Describe the pattern. Use a “smooth’’ fit if your software has this capability. Otherwise, find the mean price for each
Modeling the means. Following the pattern in Example 11.21, use the output in Figure 11.19 to write the equations for the predicted mean price for the following:(a) Homes with 1 bathroom.(b) Homes with 1.5 bathrooms.(c) Homes with 2 bathrooms.(d) Homes with 2.5 bathrooms.(e) How can we interpret
Compare the means. Regression on a single indicator variable compares the mean responses in two groups. It is, in fact, equivalent to the pooled t test for comparing two means (Chapter 7, page 389). Use the pooled t test to compare the mean price of the homes that have three or more bedrooms with
Find the means. Using the data set for Example 11.21, find the mean price for the homes that have three or more bedrooms and the mean price for those that do not.(a) Compare these sample means with the predicted values given in Example 11.21.(b) What is the difference between the mean price of the
Predicted values. Use the quadratic regression equation in Example 11.19 to predict the price of a home that has 1750 ft2. Do the same for a home that has 2250 ft2. Compare these predictions with the ones from an analysis that uses only SqFt as an explanatory variable.
The relationship between SqFt and SqFt2. Using the data set for Example 11.19, plot SqFt2 versus SqFt. Describe the relationship. We know that it is not linear, but is it approximately linear? What is the correlation between SqFt and SqFt2? The plot and correlation demonstrate that these variables
Predicted values. Use the simple linear regression equation to obtain the predicted price for a home that has 1750 ft2. Do the same for a home that has 2250 ft2.
Plot the residuals. Obtain the residuals from the simple linear regression in the preceding example and plot them versus SqFt. Describe the plot. Does it suggest that the relationship might be curved?
Distributions. Make stemplots or histograms of the prices and of the square feet for the 44 homes in Table 11.6. Do the seven homes excluded in Example 11.17 appear unusual for this location?
Compensation and human capital. A study of bank branch manager compensation collected data on the salaries of 82 managers at branches of a large eastern U.S. bank.15 Multiple regression models were used to predict how much these branch managers were paid. The researchers examined two sets of
Canada’s Small Business Financing Program. The Canada Small Business Financing Program (CSBFP) seeks to increase the availability of loans for establishing and improving small businesses.A survey was performed to better understand the experiences of small businesses when seeking loans and the
Direct versus indirect loans. The previous four exercises describe a study of loans for buying new cars. The authors conclude that banks take higher risks with indirect loans because they do not take into account borrower characteristics when setting the loan rate. Explain how the results of the
Auto dealer loans, continued. Table 11.5 gives the estimated regression coefficient and individual t statistic for each explanatory variable in the setting of the previous exercise. The t-values are given without the sign, assuming that all tests are two-sided.(a) What are the degrees of freedom of
Auto dealer loans. The previous two exercises describe auto loans made directly by a bank. The researchers also looked at 5664 loans made indirectly—that is, through an auto dealer. They again used multiple regression to predict the interest rate using the same set of 13 explanatory variables.(a)
Bank auto loans, continued. Table 11.4 gives the coefficients for the fitted model and the individual t statistic for each explanatory variable in the study described in the previous exercise. The t-values are given without the sign, assuming that all tests are two-sided.(a) State the null and
Bank auto loans. Banks charge different interest rates for different loans. A random sample of 2229 loans made by banks for the purchase of new automobiles was studied to identify variables that explain the interest rate charged. A multiple regression was run with interest rate as the response
Game-day spending. Game-day spending (ticket sales and food and beverage purchases) is critical for the sustainability of many professional sports teams.In the National Hockey League (NHL), nearly half the franchises generate more than two-thirds of their annual income from game-day spending.
Effect of a potential outlier. Refer to the previous exercise. MOVIES(a) There is one movie that has a much larger total U.S.box office revenue than predicted. Which is it, and how much more revenue did it obtain compared with that predicted?(b) Remove this movie and redo the multiple
Checking the model assumptions. Statistical inference requires us to make some assumptions about our data. These should always be checked prior to drawing conclusions.For brevity, we did not discuss this assessment for the movie revenue data of Section 11.2, so let’s do it here. MOVIES(a) Obtain
Discrimination at work? A survey of 457 engineers in Canada was performed to identify the relationship of race, language proficiency, and location of training in finding work in the engineering field. In addition, each participant completed the Workplace Prejudice and Discrimination Inventory
Inference basics. You run a multiple regression with 22 cases and four explanatory variables. The ANOVA table includes the sums of squares SSR 5 84 and SSE 5 127.(a) Find the F statistic for testing the null hypothesis that the regression coefficients for the four explanatory variables are all
Inference basics. You run a multiple regression with 54 cases and three explanatory variables.(a) What are the degrees of freedom for the F statistic for testing the null hypothesis that all three of the regression coefficients for the explanatory variables are zero?(b) Software output gives MSE 5

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