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Solution Manual for Basic Business Statistics, 14th Edition

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    Table of Contents Teaching Tips...................................................................................................................................1 Chapter 1 Defining and Collecting Data............................................................................................... 39 Chapter 2 Organizing and Visualizing Variables ................................................................................. 47 Chapter 3 Numerical Descriptive Measures ....................................................................................... 151 Chapter 4 Basic Probability ................................................................................................................ 195 Chapter 5 Discrete Probability Distributions ...................................................................................... 205 Chapter 6 The Normal Distribution and Other Continuous Distributions .......................................... 237 Chapter 7 Sampling Distributions....................................................................................................... 269 Chapter 8 Confidence Interval Estimation.......................................................................................... 293 Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests.................................................. 331 Chapter 10 Two-Sample Tests............................................................................................................. 373 Chapter 11 Analysis of Variance .......................................................................................................... 433 Chapter 12 Chi-Square and Nonparametric Tests ................................................................................ 461 Chapter 13 Simple Linear Regression .................................................................................................. 489 Chapter 14 Introduction to Multiple Regression .................................................................................. 539 Chapter 15 Multiple Regression Model Building ................................................................................. 591 Chapter 16 Time-Series Forecasting..................................................................................................... 651 Chapter 17 Business Analytics ............................................................................................................. 721 Chapter 18 A Roadmap for Analyzing Data ......................................................................................... 757 Chapter 19 Statistical Applications in Quality Management (Online) ................................................. 819 Chapter 20 Decision Making (Online).................................................................................................. 849 Online Sections ......................................................................................................................................... 889 Instructional Tips and Solutions for Digital Cases ................................................................................... 955 The Brynne Packaging Case ..................................................................................................................... 991

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    The CardioGood Fitness Case .................................................................................................................. 993 The Choice Is Yours/More Descriptive Choices Follow-up Case .......................................................... 1105 The Clear Mountain State Student Surveys Case.................................................................................... 1201 The Craybill Instrumentation Company Case ........................................................................................ 1373 The Managing Ashland MultiComm Services Case ................................................................................ 1375 The Mountain States Potato Company Case........................................................................................... 1423 The Sure Value Convenience Stores Case .............................................................................................. 1431

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    1 Teaching Tips Our Starting Point Of late, business statistics has been expanding and combining with other disciplines to form new fields of study such as business analytics. Because of these changes, business statistics has become an increasingly important part of business education. One must consistently reflect on which business statistics topics should get taught and how those topics should be taught. As authors, we seek ways to continuously improve the teaching of business statistics have always guided our efforts. We are members of the Decision Sciences Institute (DSI) and American Statistical Association (ASA) and attend their annual conferences. We are members of the DSI Data, Analytics and Statistics Instruction (DASI) Special Interest Group and are frequent presenters at DASI sessions held at annual and regional DSI meetings. We use the ASA’s Guidelines for Assessment and Instruction (GAISE) reports and combine them with our experiences teaching business statistics to a diverse student body at several large universities. What to teach and how to teach it are particularly significant questions to ask during a time of change. As an author team, we bring a unique collection of experiences that we believe helps us find the proper perspective in balancing the old and the new. Mark Berenson and David Levine were the first educators to create a business statistics textbook that discussed using statistical software and that used computer output as illustrations. They introduced many additional teaching and curricular innovations in their careers, and with David Stephan developed the first comprehensive introductory business statistics textbook that featured Microsoft Excel. Kathryn Szabat has provided statistical advice to various business and non-business communities. Her extensive background in statistics and operations research and her experiences interacting with professionals in practice guided her to develop and chair a new, interdisciplinary Business Systems and Analytics department, in response to the technology- and data-driven changes occurring in business today. David Stephan, an information system specialist, devised new courses and teaching methods for computer information systems, creating and teaching in one of the first personal computer classrooms in a large school of business. He became involved in early digital media efforts to improve education and lectured about the importance of data in a digital media, which led him to join Berenson’s and Levine’s efforts to improve statistics education and simplify interactions with statistical programs. Our work also benefits from teaching and research interests and the diversity of interests and generous contributions of our past co-author, Timothy Krehbiel.

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    2 Teaching Tips Five Guiding Principles When writing for introductory business statistics students, five principles guide us. 1. Help students see the relevance of statistics to their own careers by providing examples drawn from the functional areas in which they may be specializing. Students need a frame of reference when learning statistics, especially when statistics is not their major. That frame of reference for business students should be the functional areas of business, such as accounting, finance, information systems, management, and marketing. Each statistics topic needs to be presented in an applied context related to at least one of these functional areas. The focus in teaching each topic should be on its application in business, the interpretation of results, the evaluation of the assumptions, and the discussion of what should be done if the assumptions are violated. 2. Emphasize interpretation of statistical results over mathematical computation. Introductory business statistics courses should recognize the growing need to interpret statistical results that computerized processes create. This makes the interpretation of results more important than knowing how to execute the tedious hand calculations required to produce them. 3. Give students ample practice in understanding how to apply statistics to business. Both classroom examples and homework exercises should involve actual or realistic data as much as possible. Students should work with data sets, both small and large, and be encouraged to look beyond the statistical analysis of data to the interpretation of results in a managerial context. 4. Familiarize students with how to use statistical software to assist business decision-making. Introductory business statistics courses should recognize that programs with statistical functions are commonly found on a business decision maker’s desktop computer. Integrating statistical software into all aspects of an introductory statistics course enables the course to focus on interpretation of results instead of computations (see second point). 5. Provide clear instructions to students for using statistical applications. Books should explain clearly how to use programs such as Microsoft Excel, JMP, and Minitab with the study of statistics, without having those instructions dominate the book or distract from the learning of statistical concepts.

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    Teaching Tips 3 First Things First Chapter In a time of change, you can never know exactly what knowledge and background students bring into an introductory business statistics classroom. Add that to the need to curb the fear factor about learning statistics that so many students begin with, and there’s a lot to cover even before you teach your first statistical concept. We created “First Things First” to meet this challenge. This unit sets the context for explaining what statistics is (not what students may think!) while ensuring that all students share an understanding of the forces that make learning business statistics critically important today. Especially designed for instructors teaching with course management tools, including those teaching hybrid or online courses, “First Things First” has been developed to be posted online or otherwise distributed before the first class meets. We would argue that the most important class is the first class. First impressions are critically important. You have the opportunity to set the tone to create a new impression that the course will be important to the business education of your students. Make the following points:  This course is not a math course.  State that you will be learning analytical skills for making business decisions.  Explain that the focus will be on how statistics can be used in the functional areas of business. This book uses a systematic approach for meeting a business objective or solving a business problem. This approach goes across all the topics in the book and most importantly can be used as a framework in real world situations when students graduate. The approach has the acronym DCOVA , which stands for D efine, C ollect, O rganize, V isualize, and A nalyze.  D efine the business objective or problem to be solved and then define the variables to be studied.  C ollect the data from appropriate sources  O rganize the data  V isualize the data by developing charts  A nalyze the data by using statistical methods to reach conclusions. You can begin by emphasizing the importance of defining your objective or problem. Then, discuss the importance of operational definitions of variables to be considered and define variable, data, and statistics. Just as computers are used not just in the computer course, students need to know that statistics is used not just in the statistics course. This leads you to a discussion of business analytics in which data is used to make decisions. Make the point that analytics should be part of the competitive strategy of every

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    4 Teaching Tips organization especially when “big data”, meaning data collected in huge volumes at very fast rates, needs to be analyzed. 1. Inform the students that there is an Excel Guide, a JMP Guide, and a Minitab Guide at the end of each chapter. 2. Strongly encourage or require students to read the guide for the software they will be using as preparation for using that software with this book.

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    Teaching Tips 5 Chapter 1 You need to continue the discussion of the Define task by establishing the types of variables. Mention the importance of having an operational definition for each variable. Be sure to discuss the different types carefully because the ability to distinguish between categorical and numerical data will be crucial later in the course. Go over examples of each type of variable and have students provide examples of each type. Then, if you wish, you can cover the different measurement scales. Then move on to the C of the DCOVA approach, collecting data. Mention the different sources of data and make sure to cover the fact that data often needs to be cleaned of errors. Then, you could spend some time discussing sampling, even if it is just using the table of random numbers to select a random sample. You may want to take a bit more time and discuss the types of survey sampling methods and issues involved with survey sampling results. The Think About This essay discusses the important issue of the use of Web-based surveys. There is also a section on Data Cleaning that discusses the issues that occur in data collection. This is followed by a section on data formatting that includes the important concepts of stacking and unstacking variables and recoding variables. The last section discusses the types of errors that occur in surveys. The chapter also introduces three continuing cases related to the Managing Ashland MultiComm Services , CardioGood Fitness , and Clear Mountain State Student Surveys that appear at the end of many chapters. The Digital Cases are introduced in this chapter also. In these cases, students visit Web sites related to companies and issues raised in the Using Statistics scenarios that start each chapter. The goal of the Digital Cases is for students to develop skills needed to identify misuses of statistical information. As would be the situation with many real-world cases, in Digital Cases, students often need to sift through claims and assorted information in order to discover the data most relevant to a case task. They will then have to examine whether the conclusions and claims are supported by the data. (Instructional tips for using the Managing Ashland MultiComm Services, and Digital Cases and solutions to the Managing Ashland MultiComm Service, CardioGood Fitness, Clear Mountain State Student Surveys, and Digital Cases are included in this Instructor’s Solutions Manual .). Make sure that students read the Excel Guide and/or JMP Guide or Minitab Guide at the end of each chapter. The Workbook Excel instructions provide step-by-step instructions and live worksheets that automatically update when data changes. The PHStat Excel instructions provide instructions for using the PHStat add-in with Excel. The Analysis ToolPak instructions provide instructions for using the Analysis ToolPak, the Excel statistical add-in that is included with Microsoft Excel.

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    6 Teaching Tips Chapter 2 This chapter moves on to the organizing and visualizing steps of the DCOVA framework. If you are going to collect sample data to use in Chapters 2 and 3, you can illustrate sampling by conducting a survey of students in your class. Ask each student to collect his or her own personal data concerning the time it takes to get ready to go to class in the morning or the time it takes to get to school or home from school. First, ask the students to write down a definition of how they plan to measure this time. Then, collect the various answers and read them to the class. Then, a single definition could be provided (such as the time to get ready is the time measured from when you get out of bed to when you leave your home, recorded to the nearest minute). In the next class, select a random sample of students and use the data collected (depending on the sample size) in class when Chapters 2 and 3 are discussed. Then, move on to the Organize step that involves setting up your data in an Excel, JMP, or Minitab. Show the summary worksheet and develop tables to help you prepare charts and analyze your data. Begin your discussion for categorical data with the example on p. 43 concerning the percentage of the time millennials use different devices for watching television and then if you wish, explain that you can sometimes organize the data into a two-way table that has one variable in the row and another in the column. Continue with organizing data (but now for numerical data) by referring to the cost of a restaurant meal on p. 46. Show the simple ordered array and how a frequency distribution, percentage distribution, or cumulative distribution can summarize the raw data in a way that is more useful. Now you are ready to tackle the Visualize step. A good way of starting this part of the chapter is to display the following quote. "A picture is worth a thousand words." Students will almost certainly be familiar with Microsoft ® Word and may have already used Excel to construct charts that they have pasted into Word documents. Now you will be using Excel or JMP or Minitab to construct many different types of charts. Return to the data previously discussed on what devices millennials use to watch television and illustrate how a bar chart and pie chart can be constructed. Mention their advantages and disadvantages. A good example is to show the data on incomplete ATM transactions on p. 75 and how the Pareto chart enables you to focus on the vital few categories. If time permits, you can discuss the side-by-side bar chart for a contingency table. To examine charts for numerical variables you can either use the restaurant data previously mentioned or data that you have collected from your class. You may want to begin with a simple stem- and-leaf display that both organizes the data and shows a bar type chart. Then move on to the histogram and the various polygons, pointing out the advantages and disadvantages of each.

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    Teaching Tips 7 If time permits, you can discuss the scatter plot and the time-series plot for two numerical variables. Otherwise, you can wait until you get to regression analysis. Also, you may want to discuss how multidimensional tables allow you to see several variables simultaneously. If the opportunity is available, we believe that it is worth the time to cover Section 2.9 on Pitfalls in Organizing and Visualizing Data. This is a topic that students very much enjoy because it allows for a great deal of classroom interaction. After discussing the fundamental principles of good graphs, try to illustrate the improper display shown in Figure 2.31. Ask students what is “bad” about this figure. Follow up with a homework assignment involving Problems 2.69 – 2.73 ( USA Today is a great source). You will find that the chapter review problems provide large data sets with numerous variables. Report writing exercises provide the opportunity for students to integrate written and/or oral presentation with the statistics they have learned. The Managing Ashland MultiComm Services case enables students to examine the use of statistics in an actual business environment. The Digital Case refers to the EndRun Financial Services and claims that have been made. The CardioGood Fitness case focuses on developing a customer profile for a market research team. The Choice Is Yours Follow-up expands on the chapter discussion of the mutual funds data. The Clear Mountain State Student Survey provides data collected from a sample of undergraduate students and a separate sample of graduate students. The Excel, JMP, and Minitab Guides for this and the remaining chapters are organized according to the sections of the chapter. They are quite extensive because they cover both organizing and visualizing many different graphs. The Excel Guide includes instructions for Workbook, PHStat, and the Analysis ToolPak. Picking and choosing among these choices enables you to choose a preferred approach.

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    8 Teaching Tips Chapter 3 This chapter on descriptive numerical statistical measures represents the initial presentation of statistical symbols in the text. Students who need to review arithmetic and algebraic concepts can read Appendix A for a quick review or use appropriate texts online streaming videos or pay for study aids from third-parties such www.videoaidedinstruction.com (for which one of the authors serves as a video instructor). Once again, as with the tables and charts constructed for numerical data, it is useful to provide an interesting set of data for classroom discussion. If a sample of students was selected earlier in the semester and data concerning student time to get ready or commuting time were collected (see Chapters 1 and 2), use these data in developing the numerous descriptive summary measures in this chapter. (If they have not been developed, use other data for classroom illustration.) Discussion of the chapter begins with the property of central tendency. We have found that almost all students are familiar with the arithmetic mean (which they know as the average) and most students are familiar with the median. A good way to begin is to compute the mean for your classroom example. Emphasize the effect of extreme values on the arithmetic mean and point out that the mean is like the center of a seesaw -- a balance point. Note that you will return to this concept later when you discuss the variance and the standard deviation. You might want to introduce summation notation at this point and express the arithmetic mean in formula notation as in Equation (3.1). (Alternatively, you could wait until you cover the variance and standard deviation.) A classroom example in which summation notation is reviewed is usually worthwhile. Remind the students again that Appendix A includes a review of arithmetic and algebra and summation notation and refer them to other sources, if necessary The next statistic to compute is the median. Be sure to remind the students that the median as a measure of position must have all the values ranked in order from lowest to highest. Be sure to have the students compare the arithmetic mean to the median and explain that this tells us something about another property of data (skewness). Following the median, the mode can be briefly discussed. Once again, have the students compare this result to those of the arithmetic mean and median for your data set. If time permits, you can also discuss the geometric mean which is heavily used in finance. The completion of the discussion of central tendency leads to the second characteristic of data, variability. Mention that all measures of variation have several things in common: (1) they can never be negative, (2) they will be equal to 0 when all items are the same, (3) they will be small when there isn't much variation, and (4) they will be large when there is a great deal of variation. The first measure of variability to consider is the simplest one, the range. Be sure to point out that the range only provides information about the extremes, not about the distribution between the extremes. Point out that the range lacks one important ingredient, the ability to take into account each data value. Bring up the idea of computing the differences around the mean, but then return to the fact that as the

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    Teaching Tips 9 balance point of the seesaw, these differences add up to zero. At that point, ask the students what they can do mathematically to remove the negative sign for some of the values. Most likely, they will answer by telling you to square them (although someone may realize that the absolute value could be taken). Next, you may want to define the squared differences as a sum of squares. Now you need to have the students realize that the number of values being considered affects the magnitude of the sum of squared differences. Therefore, it makes sense to divide by the number of values and compute a measure called the variance. If a population is involved, you divide by N , the population size, but if you are using a sample, you divide by n - 1, to make the sample result a better estimate of the population variance. You can finish the development of variation by noting that because the variance is in squared units, you need to take the square root to compute the standard deviation. Another measure of variation that can be discussed is the coefficient of variation. Be sure to illustrate the usefulness of this as a measure of relative variation by using an example in which two data sets have vastly different standard deviations, but also vastly different means. A good example is one that involves the volatility of stock prices. Point out that the variation of the price should be considered in the context of the magnitude of the arithmetic mean. By changing values in the data provided, students can observe how the mean, median, and standard deviation are affected. The final measure of variation is the Z score. Point out that this provides a measure of variation in standard deviation units. You can also say that you will return to Z scores in Chapter 6 when the normal distribution will be discussed. You are now ready to move on to the third characteristic of data, shape. Be sure to clearly define and illustrate both symmetric and skewed distributions by comparing the mean and median. You may also want to briefly mention the property of kurtosis which is the relative concentration of values in the center of the distribution as compared to the tails. This statistic is provided by Excel through an Excel function or the Analysis Toolpak and by JMP or Minitab. Once these three characteristics have been discussed, you are ready to show how they can be computed using Excel, JMP, or Minitab. Now that these measures are understood, you can further explore data by computing the quartiles, the interquartile range, the five number summary, and constructing a boxplot. You begin by determining the quartiles. Reference here can be made to the standardized exams that most students have taken, and the quantile scores that they have received (97th percentile, 48th percentile, 12th percentile, …, etc.). Explain that the 1 st and 3 rd quartiles are merely two special quantiles -- the 25th and 75th, that unlike the median (the 2 nd quartile), are not at the center of the distribution. Once the quartiles have been computed, the interquartile range can be determined. Mention that the interquartile range computes the variation in the center of the distribution as compared to the difference in the extremes computed by the range.

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    10 Teaching Tips You can then discuss the five-number summary of minimum value, first quartile, median, third quartile, and maximum value. Then, you construct the boxplot. Present this plot from the perspective of serving as a tool for determining the location, variability, and symmetry of a distribution by visual inspection, and as a graphical tool for comparing the distribution of several groups. It is useful to display Figure 3.9 on page 142 that indicates the shape of the boxplot for four different distributions. Then, use PHStat or JMP or Minitab to construct a boxplot. Note that you can construct the boxplot for a single group or for multiple groups. If you desire, you can discuss descriptive measures for a population and introduce the empirical rule and the Chebyshev rule. If time permits, and you have covered scatter plots in Chapter 2, you can briefly discuss the covariance and the coefficient of correlation as a measure of the strength of the association between two numerical variables. Point out that the coefficient of correlation has the advantage as compared to the covariance of being on a scale that goes from -1 to +1. Figure 3.12 on p. 150 is useful in depicting scatter plots for different coefficients of correlation. Once again, you will find that the chapter review problems provide large data sets with numerous variables. The Managing Ashland MultiComm Services case enables students to examine the use of descriptive statistics in an actual business environment. The Digital Case continues the evaluation of the EndRun Financial Services discussed in the Digital Case in Chapter 2. The CardioGood Fitness case focuses on developing a customer profile for a market research team. More Descriptive Choices Follow- up expands on the discussion of the mutual funds data. The Clear Mountain State Student Survey provides data collected from a sample of undergraduate students and a separate sample of graduate students. The Excel Guide for the chapter includes instructions on using different Excel functions to compute various statistics. Alternatively, you can use PHStat or the Analysis ToolPak to compute a list of statistics. PHStat can be used to construct a boxplot. Or you can use JMP or Minitab.

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    Teaching Tips 11 Chapter 4 The chapter on probability represents a bridge between the descriptive statistics already covered and the topics of statistical inference, regression, time series, and quality improvement to be covered in subsequent chapters. In many traditional statistics courses, often a great deal of time is spent on probability topics that are of little direct applicability in basic statistics. The approach in this text is to cover only those topics that are of direct applicability in the remainder of the text. You need to begin with a relatively concise discussion of some probability rules. Essentially, students really just need to know that (1) no probability can be negative, (2) no probability can be more than 1, and (3) the sum of the probabilities of a set of mutually exclusive events adds to 1.0. Students often understand the subject best if it is taught intuitively with a minimum of formulas, with an example that relates to a business application shown as a two-way contingency table (see the Using Statistics example). If desired, you can use Workbook Excel or PHStat to compute probabilities from the contingency table. Once these basic elements of probability have been discussed, if there is time and you desire, conditional probability and Bayes’ theorem can be covered. The Think About This concerning email SPAM is a wonderful way of helping students realize the application of probability to everyday life. In addition, you may wish to spend a bit of time going over counting rules, especially if the binomial distribution will be covered in Chapter 5. Be aware that in a one-semester course where time is particularly limited, these topics may be of marginal importance. The Digital Case in this chapter extends the evaluation of the EndRun Financial Services to consider claims made about various probabilities. The CardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain State Student Survey each involve developing contingency tables to be able to compute and interpret conditional and marginal probabilities.

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    12 Teaching Tips Chapter 5 Now that the basic principles of probability have been discussed, the probability distribution is developed and the expected value and variance (and standard deviation) are computed and interpreted. Given that a probability distribution has been defined, you can now discuss some specific distributions. Although every introductory course undoubtedly covers the normal distribution to be discussed in Chapter 6, the decision about whether to cover the binomial or Poisson distributions is matter of personal choice and depends on whether the course is part of a two-course sequence. If the binomial distribution is covered, an interesting way of developing the binomial formula is to follow the Using Statistics example that involves an accounting information system. Note, in this example, the value for p is 0.10. (It is best not to use an example with p = 0.50 because this represents a special case). The discussion proceeds by asking how you could get three tagged order forms in a sample of 4. Usually a response will be elicited that provides three items of interest out of four selections in a particular order such as Tagged Tagged Not Tagged Tagged. Ask the class, what would be the probability of getting Tagged on the first selection? When someone responds 0.1, ask them how they found that answer and what would be the probability of getting Tagged on the second selection. When they answer 0.1 again, you will be able to make the point that in saying 0.1 again, they are assuming that the probability of Tagged stays constant from trial to trial. When you get to the third selection and the students respond 0.9, point out that this is a second assumption of the binomial distribution -- that only two outcomes are possible -- in this case Tagged and Not Tagged, and the sum of the probabilities of Tagged and Not Tagged must add to 1.0. Now you can compute the probability of three out of four in this order by multiplying (0.1)(0.1)(0.9)(0.1) to get 0.0036. Ask the class if this is the answer to the original question. Point out that this is just one way of getting three Tagged out of four selections in a specific order, and, that there are four ways to get three Tagged out of four selections This leads to the development of the binomial formula Equation (5.4). You might want to do another example at this point that calls for adding several probabilities such as three or more Tagged, less than three Tagged, etc. Complete the discussion of the binomial distribution with the computation of the mean and standard deviation of the distribution. Be sure to point out that for samples greater than five, computations can become unwieldy and the student should use PHStat, an Excel function, the binomial tables (see the online Binomial.pdf tables), JMP, or Minitab. Once the binomial distribution has been covered, if time permits, other discrete probability distributions can be presented. If you cover the Poisson distribution, point out the distinction between the binomial and Poisson distributions. Note that the Poisson is based on an area of opportunity in which you are counting occurrences within an area such as time or space. Contrast this with the binomial distribution in which each value is classified as of interest or not of interest. Point out the equations for the mean and

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    Teaching Tips 13 standard deviation of the Poisson distribution and indicate that the mean is equal to the variance. Because the computation of probabilities from these discrete probability distributions can become tedious for other than small sample sizes, it is important to discuss PHStat, an Excel function the Poisson tables (see the online Poisson.pdf tables) or JMP or Minitab. The covariance of a probability distribution is included as an online section. The hypergeometric distribution is also included as an online section. The Managing Ashland MultiComm Services case for this chapter relates to the binomial distribution. The Digital Case involves the expected value and standard deviation of a probability distribution and applications of the covariance in finance.

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