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Questions and Answers of Business Statistics

Proportion of automobiles sold during the last quarter by eight major manufacturersMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and
Auto manufacturers are sensitive to the color preferences of consumers. Would they like to know the modal preference or the median preference?
A magazine wants a graphic that presents the sales of cars in the United States, broken down by the major manufacturers. To get the attention of readers, the graphic will show a car representing the
The data for this exercise derive from a sample of 5,000 visits to amazon.com, and, as in the example in this chapter, the data for each visit list the host that linked to Amazon. The key difference
The U.S. Census Bureau occasionally surveys business owners and learns which firms are predominantly owned by women. These data are a portion of the results reported in 2010 from the 2007 Survey of
List the criteria and model selection procedures we use to compare regression models.
List the tools that we use to identify an outlier with respect to its y value and/or x values.
For each of the following cases, use the indicated residual plots to check for any violations of the regression assumptions.a. The Tasty Sub Shop Case: For the model relating Revenue to Population
What two values does the dependent variable equal in logistic regression? What do these values represent?
When is neural network modeling most useful?
How do we define the output layer function g(L)?
United Oil is attempting to develop a middle-grade gasoline that will deliver high gasoline mileages. As part of its development process, United Oil will study the effect of three middle-grade
Although natural gas is currently inexpensive and nuclear power currently (and perhaps deservedly) does not have a good reputation, it is possible that more nuclear power plants will be constructed
Discuss how we model no trend and a linear trend.
In this exercise we consider annual U.S. lumber production over 30 years. The data were obtained from the U.S. Department of Commerce Survey of Current Business and are presented in Table 15.5. (The
Referring to the situation of Exercise 15.3, the mean and the standard deviation of the lumber production values can be calculated to be y̅ = 35,651.9 and s = 2,037.3599. Find a point forecast of
Use the Durbin€“Watson statistic given at the bottom of the Minitab output in Figure 15.9(c) to assess whether there is positive auto-correlation.Figure 15.9(c) SE Coef T-Value P-Value
Explain how the multiplicative decomposition model estimates seasonal factors.
Explain how the multiplicative decomposition method estimates the trend effect.
Discuss how the multiplicative decomposition method makes point forecasts of future time series values.
Find and identify the four seasonal factors for quarters 1, 2, 3, and 4.International Machinery, Inc., produces a tractor and wishes to use quarterly tractor sales data observed in the last four
Compute an approximate 95 percent prediction interval forecast of tractor sales for each of the quarters next year. Use the fact that the half-lengths of 95 percent prediction intervals for the
In general, when is it appropriate to use exponential smoothing?
What is the purpose of a smoothing constant in exponential smoothing?
When do we use double exponential smoothing?
When do we use the multiplicative Winters’ method?
Figure 15.20 gives the Minitab output of using double exponential smoothing in month 20 to forecast watch sales in months 21 through 26. Here we have used Minitab€™s default option that
Figure 15.21 on the next page gives the Minitab output of using multiplicative Winters€™ method in month 168 to forecast the monthly hotel room averages in months 169 through 180. Here we
Consider the monthly international passenger totals in Table 15.8 on page 690. Use Minitab and Winters€™ method in month 132 to find point predictions of and 95 percent prediction intervals
What is the MAD? What is the MSD? What is the MAPE? How do we use these quantities?
Why does the MSD penalize a forecasting method much more for large forecast errors than for small forecast errors?
Which method—method A or method B—gives the smallest MAD? The smallest MSD? The smallest MAPE?Compare two forecasting methods—method A and method B. Suppose that method A gives the point
Explain the difference between a simple index and an aggregate index.
Explain the difference between a Laspeyres index and a Paasche index.
Referring to the discussion of Figure 15.22, the CPI-U for March 2011 was 223.47, and the CPI-U for October 1963 was 30. Interpret these CPI-U€™s. FIGURE 15.22 Plot of the Monthly CPI-U
Recall that Table 15.16 gives the price of a gallon of regular gasoline in the United States (in dollars) for the years 2003 through 2011. Table 15.20 gives the price of a gallon of regular gasoline
Table 15.24 gives quarterly sales (in thousands of cases) of Tiger Sports Drink over the previous eight years. Plot the data and use an appropriate forecasting technique to find point predictions of
Write a paragraph explaining how common causes of process variation differ from assignable causes of process variation.
Explain (1) the purpose of an x̅ chart, (2) the purpose of an R chart, (3) why both charts are needed.
Explain why the initial control limits calculated for a set of subgrouped data are called “trial control limits.”
In an issue of Quality Progress, Gunter presents several control charts. Four of these charts are reproduced in Figure 16.17. For each chart, find any evidence of a lack of statistical control (that
In the book Tools and Methods for the Improvement of Quality, Gitlow, Gitlow, Oppenheim, and Oppenheim present several control charts in a discussion and exercises dealing with pattern analysis.
Write a short paragraph explaining why a process that is in statistical control is not necessarily capable of meeting customer requirements (specifications).
Explain the interpretation of the natural tolerance limits for a process. What assumptions must be made in order to properly make this interpretation? How do we check these assumptions?
For each of the following, explaina. Why it is important to have leeway between the natural tolerance limits and the specification limits.b. What is meant by the sigma level capability for a
Suppose that x̅ and R charts based on subgroups of size 3 are used to monitor the moisture content of a type of paper. The x̅ and R charts are found to be in statistical control with x̅̅ = 6.0
Suppose that a normally distributed process (centered at target) has three sigma capability. If the process shifts 1.5 sigmas to the right, show that the process will produce defective products at a
In your own words, define a nonconforming unit.
Explain the purpose behind constructing (a) A cause-and effect diagram(b) A defect concentration diagram.
In an issue of Quality Progress, Hoexter and Julien discuss the quality of the services delivered by law firms. One aspect of such service is the quality of attorney€“client communication.
What is a nonparametric test? Why would such a test be particularly useful when we must take a small sample?
When we perform the sign test, we use the sample data to compute a p-value. What probability distribution is used to compute the p-value? Explain why.
Consider the following sample of five chemical yields:a. Use this sample to test H0: Md = 800 versus Ha: Md ‰ 800 by setting Î± = .01.b. Use this sample to test H0: Md = 750
A local newspaper randomly selects 20 patrons of the Springwood Restaurant on a given Saturday night and has each patron rate the quality of his or her meal as 5 (excellent), 4 (good), 3 (average), 2
Explain the circumstances in which we use the Wilcoxon rank sum test.
Identify the parametric test corresponding to the Wilcoxon rank sum test. What assumption is needed for the validity of this parametric test (and not needed for the Wilcoxon rank sum test)?
A loan officer at a bank wishes to compare the new car loan rates charged at banks in Ohio with the new car loan rates of Ohio credit unions. Two independent random samples of bank rates and credit
Explain the circumstances in which we use the Wilcoxon signed ranks test.
Identify the parametric test corresponding to the Wilcoxon signed ranks test. What assumption is needed for the validity of the parametric test (and not needed for the Wilcoxon signed ranks test)?
Explain the circumstances in which we use the Kruskal–Wallis H test.
Identify the parametric test corresponding to the Kruskal–Wallis H test.
What are the assumptions needed for the validity of the parametric test identified in Exercise 17.21 that are not needed for the Kruskal–Wallis H test?Exercise 17.21Identify the parametric test
Use the Kruskal€“Wallis H test to compare display panels A, B, and C using the data in Table 17.8. Use Î± = .05.Table 17.8Use the given independent samples to perform the
Use the Kruskal€“Wallis H test to compare bottle designs A, B, and C using the data in Table 17.9. Use Î± = .01.Table 17.Use the given independent samples to perform the
Use the Kruskal€“Wallis H test and the Minitab output in Figure 17.5 to compare the bottom (B), middle (M), and top (T) display heights using the data in Table 17.10. Use Î± =
Explain the circumstances in which we use Spearman’s rank correlation coefficient.
A drug company wishes to compare the effects of three different drugs (X, Y, and Z) that are being developed to reduce cholesterol levels. Each drug is administered to six patients at the recommended
Table 17.16 gives the median 2009 and 2010 prices for used homes (in thousands of dollars) for six randomly selected U.S. housing markets. Use a nonparametric test to attempt to show that housing
During 2011 a company implemented a number of policies aimed at reducing the ages of its customers€™ accounts. In order to assess the effectiveness of these measures, the company randomly
Explain the differences between(a) Decision making under certainty,(b) Decision making under uncertainty,(c) Decision making under risk.
Explain how to use the(a) Maximin criterion,(b) Maximax criterion,(c) Expected monetary value criterion.
Explain how to find the expected value of perfect information.
Find the best alternative (and the resulting payoff) in the given payoff table if it is known with certainty that demand will bea. Low.b Medium.c High.The example involves a capacity-planning problem
Given the payoff table, find the alternative that would be chosen using the maximin criterion.The example involves a capacity-planning problem in which a company must choose to build a small, medium,
Given the payoff table, find the alternative that would be chosen using the maximax criterion.The example involves a capacity-planning problem in which a company must choose to build a small, medium,
Suppose that the company assigns prior probabilities of .3, .5, and .2 to low, moderate, and high demands, respectively.a. Find the expected monetary value for each alternative (small, medium, and
Construct a decision tree for the information in the payoff table assuming that the prior probabilities of low, moderate, and high demands are, respectively, .3, .5, and .2.The example involves a
For the information in the payoff table finda. The expected payoff under certainty.b. The expected value of perfect information, EVPI.The example involves a capacity-planning problem in which a
A firm wishes to choose the location for a new factory. Profits obtained will depend on whether a new railroad spur is constructed to serve the town in which the new factory will be located. The
Construct a decision tree for the information given in Exercises 18.10 and 18.11.Exercise 18.10 and Exercise 18.11 No New Railroad Spur New Railroad Alternatives Spur Built $1* $14 Location A
Refer to the information given in Exercise 18.10. Using the probabilities of .60 for a new railroad spur and .40 for no new railroad spur.a. Compute the expected monetary value for each location.b.
Figure 18.3 gives a decision tree presented in the book Production/Operations Management by William J. Stevenson. Use this tree diagram to do the following:a. Find the expected monetary value for
Identify and list each of the following for the investor€™s decision problem:a. The investor€™s alternative actions.b. The states of nature.c. The possible results of sampling
Carry out a prior analysis of the investor€™s decision problem. That is, determine the investment choice that should be made and find the expected monetary value of that choice assuming
Carry out a posterior analysis of the investor€™s decision problem. That is, determine the investment choice that should be made and find the expected monetary value of that choice
Carry out a preposterior analysis of the investor€™s decision problem by finding:a. The expected monetary value associated with consulting the economist; that is, find the EPS.b. The
Identify and list each of the following for the control device situation:a. The firm’s alternative actions.b. The states of nature.c. The possible results of sampling (that is, of information
Construct a decision tree for a prior analysis of the control device situation. Then determine whether the engineers should be sent, assuming that the piece of test equipment is not employed to check
Set up probability revision tables to:a. Find the probability that the test equipment “reads in,” and find the posterior probabilities of in alignment and out of alignment given that the test
Carry out a posterior analysis of the control device problem. That is, decide whether the engineers should be sent, and find the expected monetary value associated with either sending or not sending
What is a utility?
Carry out a preposterior analysis of the control device problem by finding:a. The expected monetary value associated with using the test equipment; that is, find the EPS.b. The expected monetary
Suppose that a decision maker has the opportunity to invest in an oil well drilling operation that has a .3 chance of yielding a profit of $1,000,000, a .4 chance of yielding a profit of $400,000,
Consider Exercise 18.31. Find the expected utility of the oil well drilling operation. Find the expected utility of not investing. What should the decision maker do if he/she wishes to maximize
Write out the payoff table for the investor€™s decision problem.An Introduction to Decision Analysis, 2nd ed., Robert T. Clemen presents an example in which an investor wishes to choose
In the book Making Hard Decisions: An Introduction to Decision Analysis, Robert T. Clemen presents a decision tree for a research and development decision (note that payoffs are given in millions of
In the book Production/Operations Management, William J. Stevenson presents a decision tree concerning a firm€™s decision about the size of a production facility. This decision tree is
Consider the decision tree in Figure 18.9 and the situation described in Exercise 18.34. Suppose that a marketing research study can be done to obtain more information about whether demand will be
Discuss the purpose of differencing.
Explain how we use the SAC and SPAC.

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