Solution Manual for Business Statistics: A First Course, 7th Edition

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’SSOLUTIONSMANUALPINNGNorthern Arizona UniversityBUSINESSSTATISTICS:AFIRSTCOURSESEVENTHEDITIONDavid LevineBaruch College, City University of New YorkKathryn SzabatLa Salle UniversityDavid StephanTwo Bridges Instructional Technology

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Table of ContentsTeaching Tips...................................................................................................................................1Chapter 1Defining and Collecting Data............................................................................................... 31Chapter 2Organizing and Visualizing Variables ................................................................................. 37Chapter 3Numerical Descriptive Measures ....................................................................................... 134Chapter 4Basic Probability ................................................................................................................ 174Chapter 5Discrete Probability Distributions...................................................................................... 183Chapter 6The Normal Distribution .................................................................................................... 211Chapter 7Sampling Distributions....................................................................................................... 240Chapter 8Confidence Interval Estimation.......................................................................................... 260Chapter 9Fundamentals of Hypothesis Testing: One-Sample Tests.................................................. 291Chapter 10Two-Sample Tests and One-Way ANOVA ...................................................................... 334Chapter 11Chi-Square Tests ................................................................................................................ 424Chapter 12Simple Linear Regression .................................................................................................. 450Chapter 13Multiple Regression ........................................................................................................... 489Chapter 14Statistical Applications in Quality Management (Online) ................................................. 536Instructional Tips and Solutions for Digital Cases............................................................. 570TheManaging Ashland MultiComm ServicesCase........................................................... 594TheBrynne PackagingCase .............................................................................................. 635TheCardioGood FitnessCase ........................................................................................... 637TheChoice Is Yours/More Descriptive Choices Follow-upCase...................................... 755TheClear Mountain State Student SurveysCase............................................................... 815TheHarnswell Sewing Machine CompanyCase ............................................................... 952TheSure Value Convenience StoresCase.......................................................................... 954

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Teaching Tips1Teaching Tips forBusiness Statistics: A First Course 7thEd.Our Starting PointOver a generation ago, advances in “data processing” led to new business opportunities as firstcentralized and then desktop computing proliferated. The Information Age was born. Computerscience became much more than just an adjunct to a mathematics curriculum, and whole new fields ofstudies, such as computer information systems, emerged.More recently, further advances in information technologies have combined with dataanalysis techniques to create new opportunities in what is more datasciencethan dataprocessingorcomputerscience. The world of business statistics has grown larger, bumping into other disciplines.And, in a reprise of something that occurred a generation ago, new fields of study, this time withnames such as informatics, data analytics, and decision science, have emerged.This time of change makes what is taught in business statistics and how it is taught all the morecritical. These new fields of study all share statistics as a foundation for further learning. We areaccustomed to thinking about change, as seeking ways to continuously improve the teaching ofbusiness statistics have always guided our efforts. We actively participate in Decision SciencesInstitute (DSI), American Statistical Association (ASA), and Making Statistics More Effective inpSchools and Business (MSMESB) conferences. We use the ASA’s Guidelines for Assessment andInstruction (GAISE) reports and combine them with our experiences teaching business statistics to adiverse student body at several large universities.What to teach and how to teach it are particularly significant questions to ask during a time ofchange. As an author team, we bring a unique collection of experiences that we believe helps us findthe proper perspective in balancing the old and the new. Our lead author, David M. Levine, was thefirst educator, along with Mark L. Berenson, to create a business statistics textbook that discussedusing statistical software and incorporated “computer output” as illustrations—just the first of manyteaching and curricular innovations in his many years of teaching business statistics.David Stephan

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Teaching Tips2is the principal at Two Bridges Instructional Technology. As a CIS instructor at BaruchCollege, he pioneered teaching software in a business context, bringing computers intoclassrooms, and developed a new-media learning environment as part of a U.S. Dept. ofEducation FIPSE grant. He is also the developer of PHStat, the Excel add-in for statisticsstudents.Our newest co-author, Kathryn A. Szabat, has provided statistical advice to variousbusiness and non-business communities. Her background in statistics and operations research and herexperiences interacting with professionals in practice have guided her, as departmental chair, indeveloping a new, interdisciplinary academic department, Business Systems and Analytics, inresponse to the technology- and data-driven changes in business today. We also benefit from ourmany years teaching undergraduate business subjects and the diversity of interests and efforts of ourpast co-authors, Mark Berenson and Timothy Krehbiel.Educational PhilosophyAs in prior editions ofBusiness Statistics: A First Course, we are guided by these key learningprinciples:1.Help students see the relevance of statistics to their own careers by providing examplesdrawn from the functional areas in which they may be specializing.Students need a frame ofreference when learning statistics, especially when statistics is not their major. That frame ofreference for business students should be the functional areas of business, such as accounting,finance, information systems, management, and marketing. Each statistics topic needs to bepresented in an applied context related to at least one of these functional areas. The focus inteaching each topic should be on its application in business, the interpretation of results, theevaluation of the assumptions, and the discussion of what should be done if the assumptions areviolated.2.Emphasize interpretation of statistical results over mathematical computation.Introductory

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Teaching Tips3business statistics courses should recognize the growing need tointerpretstatistical results thatcomputerized processes create. This makes the interpretation of results more important thanknowing how to execute the tedious hand calculations required to produce them.3.Give students ample practice in understanding how to apply statistics to business.Bothclassroom examples and homework exercises should involve actual or realistic data as much aspossible. Students should work with data sets, both small and large, and be encouraged to lookbeyond 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 functionsare commonly found on a business decision maker’s desktop computer.Integrating statisticalsoftwareinto all aspects of an introductory statistics course allows the course to focus oninterpretation of results instead of computations (see point 2).5.Provide clear instructions to students for using statistical applications.Books should explainclearly how to use programs such as Microsoft Excel and Minitab with the study of statistics,without having those instructions dominate the book or distract from the learning of statisticalconcepts.

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Teaching Tips4Getting Started: Important Things to Learn FirstIn a time of change, you can never know exactly what knowledge and background students bring intoan introductory business statistics classroom. Add that to the need to curb the fear factor aboutlearning statistics that so many students begin with, and there’s a lot to cover even before you teachyour first statistical concept.We created “Getting Started: Important Things to Learn First” to meet this challenge. This unitsets the context for explaining what statistics is (not what students may think!) while ensuring that allstudents share an understanding of the forces that make learning business statistics criticallyimportant today. Especially designed for instructors teaching with course management tools,including those teaching hybrid or online courses, “Getting Started” has been developed to be postedonline or otherwise distributed before the first class section.We would argue that the most important class is the first class. First impressions are criticallyimportant. You have the opportunity to set the tone to create a new impression that the course will beimportant 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 ofbusiness.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 frameworkin real world situations when students graduate. The approach has the acronymDCOVA, whichstands forDefine,Collect,Organize,Visualize, andAnalyze.•Define the business objective or problem to be solved and then define the variables to bestudied.•Collect the data from appropriate sources•Organize the data

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Teaching Tips5•Visualize the data by developing charts•Analyze 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 isused not just in the statistics course. This leads you to a discussion of business analytics in which datais used to make decisions. Make the point that analytics should be part of the competitive strategy ofevery organization especially since “big data”, meaning data collected in huge volumes at very fastrates, needs to be analyzed.Inform the students that there is an Excel Guide and a Minitab Guide at the end of each chapter.Strongly encourage or require students to read the Excel Guide and/or the Minitab Guide at the end ofthis chapter so that they will be ready to use Excel and/or Minitab with this book.

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Teaching Tips6Chapter 1You 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 thedifferent types carefully since the ability to distinguish between categorical and numerical data willbe crucial later in the course. Go over examples of each type of variable and have students provideexamples of each type.Then move on to the C of the DCOVA approach, collecting data. Mention the differentsources 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 randomnumbers to select a random sample. You may want to take a bit more time and discuss the types ofsurvey sampling methods and issues involved with survey sampling results. TheThink about Thisessay discusses the important issue of the use of Web-based surveys.The chapter also introduces three continuing cases related to theManaging AshlandMultiComm Services,CardioGood Fitness, andClear Mountain State Student Surveysthat appear atthe 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 thatstart each chapter. The goal of the Digital cases is for students to develop skills needed to identifymisuses of statistical information. As would be the situation with many real world cases, in Digitalcases, students often need to sift through claims and assorted information in order to discover the datamost relevant to a case task. They will then have to examine whether the conclusions and claims aresupported by the data. (Instructional tips for using theManaging Ashland MultiComm Services,andDigital cases and solutions to theManaging Ashland MultiComm Service,CardioGood Fitness, ClearMountain State Student Surveys, and Digital cases are included in this’s SolutionsManual.).Make sure that students read the Excel Guide and/or Minitab Guide at the end of eachchapter. Section EG.1 on page 8 explains the different type of Excel instructions. TheIn-Depth Excelinstructions provide step-by-step instructions and live worksheets that automatically update when datachanges. ThePHStatadd-in instructions provide instructions for using the PHStat add-in.AnalysisToolPakinstructions provide instructions for using the Analysis ToolPak, the Excel add-in packagethat is included with many versions of Excel.

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Teaching Tips7Chapter 2This chapter moves on to the organizing and visualizing steps of the DCOVA framework. Ifyou are going to collect sample data to use in Chapters 2 and 3, you can illustrate sampling byconducting a survey of students in your class. Ask each student to collect his or her own personal dataconcerning the time it takes to get ready to go to class in the morning or the time it takes to get toschool or home from school. First, ask the students to write down a definition of how they plan tomeasure this time. Then, collect the various answers and read them to the class. Then, a singledefinition could be provided (such as the time to get ready is the time measured from when you getout of bed to when you leave your home, recorded to the nearest minute). In the next class, select arandom sample of students and use the data collected (depending on the sample size) in class whenChapters 2 and 3 are discussed.Then, move on to the Organize step that involves setting up your data in an Excel or Minitabworksheet and develop tables to help you prepare charts and analyze your data. Begin your discussionfor categorical data with the example on p. 33 concerning the main reason young adults shop online.Show the summary table and then if you wish, explain that you can sometimes organize the data intoa 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 arestaurant meal on p. 37. Show the simple ordered array and how a frequency distribution, percentagedistribution, 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 chapteris 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 toconstruct charts that they have pasted into Word documents. Now you will be using Excel or Minitabto construct many different types of charts. Return to the data previously discussed on why youngadults shop online and illustrate how a bar chart and pie chart can be constructed. Mention theiradvantages and disadvantages. A good example is to show the data on incomplete ATM transactionson p. 48 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 previouslymentioned or data that you have collected from your class. You may want to begin with a simplestem-and-leaf display that both organizes the data and shows a bar type chart. Then move on to thehistogram and the various polygons, pointing out the advantages and disadvantages of each.

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Teaching Tips8If time permits, you can discuss the scatter plot and the time-series plot for two numericalvariables. Otherwise, you can wait until you get to regression analysis. Also, you may want to discusshow multidimensional tables allow you to see several variables simultaneously and to drill down todiscover patterns that were not available in a simple table.If the opportunity is available, we believe that it is worth the time to cover Section 2.7 onChallenges in Organizing and Visualizing Data. This is a topic that students very much enjoy since itallows for a great deal of classroom interaction. After discussing the fundamental principles of goodgraphs, try to illustrate some of the improper displays shown in Figures 2.20 – 2.24. Ask studentswhat is “bad” about these figures. Follow up with a homework assignment involving Problems 2.70 –2.75 (USA Todayis a great source).You will find that the chapter review problems provide large data sets with numerousvariables. Report writing exercises provide the opportunity for students to integrate written and/ororal presentation with the statistics they have learned.TheManaging Ashland MultiComm Servicescase enables students to examine the use ofstatistics in an actual business environment. The Digital case refers to the EndRun Financial Servicesand claims that have been made. TheCardioGood Fitnesscase focuses on developing a customerprofile for a market research team.The ChoiceIsYours Follow-upexpands on the chapter discussionof the mutual funds data. TheClear Mountain State Student Surveyprovides data collected from asample of undergraduate students and a separate sample of graduate students.The Excel Guide and the Minitab Guide for this and the remaining chapters are organizedaccording to the sections of the chapter. They are quite extensive since they cover both organizingand visualizing many different graphs. The Excel Guide includes instructions for In-Depth Excel,PHStat, and the Analysis ToolPak. Pick and allows you to choose the approaches that you prefer.

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Teaching Tips9Chapter 3This chapter on descriptive numerical statistical measures represents the initial presentationof statistical symbols in the text. Students who need to review arithmetic and algebraic concepts maywish to refer to Appendix A for a quick review or to appropriate texts (seewww.pearson.com) orvideos (www.videoaidedinstruction.com). Once again, as with the tables and charts constructed fornumerical data, it is useful to provide an interesting set of data for classroom discussion. If a sampleof students was selected earlier in the semester and data concerning student time to get ready orcommuting time were collected (see Chapters 1 and 2), use these data in developing the numerousdescriptive summary measures in this chapter. (If they have not been developed, use other data forclassroom illustration.)Discussion of the chapter begins with the property of central tendency. We have found thatalmost all students are familiar with the arithmetic mean (which they know as the average) and moststudents are familiar with the median. A good way to begin is to compute the mean for yourclassroom example. Emphasize the effect of extreme values on the arithmetic mean and point out thatthe mean is like the center of a seesaw -- a balance point. Note that you will return to this conceptlater when you discuss the variance and the standard deviation. You might want to introducesummation 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.) Aclassroom example in which summation notation is reviewed is usually worthwhile. Remind thestudents again that Appendix A includes a review of arithmetic and algebra and summation notation[or refer them to other text sources such as those found atwww.pearson.comor videos (seewww.videoaidedinstruction.com)].The next statistic to compute is the median. Be sure to remind the students that the median asa measure of position must have all the values ranked in order from lowest to highest. Be sure to havethe students compare the arithmetic mean to the median and explain that this tells us something aboutanother property of data (skewness). Following the median, the mode can be briefly discussed. Onceagain, have the students compare this result to those of the arithmetic mean and median for your dataset.The completion of the discussion of central tendency leads to the second characteristic ofdata, variability. Mention that all measures of variation have several things in common: (1) they cannever be negative, (2) they will be equal to 0 when all items are the same, (3) they will be small whenthere isn't much variation, and (4) they will be large when there is a great deal of variation.

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Teaching Tips10The first measure of variability to consider is the simplest one, the range. Be sure to point outthat the range only provides information about the extremes, not about the distribution between theextremes.Point out that the range lacks one important ingredient, the ability to take intoaccount each data value. Bring up the idea of computing the differences around the mean, but thenreturn to the fact that as the balance point of the seesaw, these differences add up to zero. At thatpoint, ask the students what they can do mathematically to remove the negative sign for some of thevalues. Most likely, they will answer by telling you to square them (although someone may realizethat the absolute value could be taken). Next, you may want to define the squared differences as asum of squares. Now you need to have the students realize that the number of values being consideredaffects the magnitude of the sum of squared differences. Therefore, it makes sense to divide by thenumber of values and compute a measure called the variance. If a population is involved, you dividebyN, the population size, but if you are using a sample, you divide byn- 1, to make the sample resulta better estimate of the population variance. You can finish the development of variation by notingthat since the variance is in squared units, you need to take the square root to compute the standarddeviation.Another measure of variation that can be discussed is the coefficient of variation. Be sure toillustrate the usefulness of this as a measure of relative variation by using an example in which twodata sets have vastly different standard deviations, but also vastly different means. A good example isone that involves the volatility of stock prices. Point out that the variation of the price should beconsidered in the context of the magnitude of the arithmetic mean.The final measure of variation is theZscore. Point out that this provides a measure ofvariation in standard deviation units. You can also say that you will return toZscores in Chapter 6when the normal distribution will be discussed.You are now ready to move on to the third characteristic of data, shape. Be sure to clearlydefine 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 ofvalues in the center of the distribution as compared to the tails. This statistic is provided by Excelthrough an Excel function or the Analysis Toolpak and by Minitab. Once these three characteristicshave been discussed, you are ready to show how they can be computed using Excel or Minitab.Now that these measures are understood, you can further explore data by computing thequartiles, the interquartile range, the five number summary, and constructing a boxplot. You begin bydetermining the quartiles. Reference here can be made to the standardized exams that most studentshave taken, and the quantile scores that they have received (97th percentile, 48th percentile, 12thpercentile …, etc.). Explain that the 1stand 3rdquartiles are merely two special quantiles -- the 25th

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Teaching Tips11and 75th, that unlike the median (the 2ndquartile), are not at the center of the distribution.Once thequartiles have been computed, the interquartile range can be determined. Mention that theinterquartile range computes the variation in the center of the distribution as compared to thedifference in the extremes computed by the range.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 theperspective of serving as a tool for determining the location, variability, and symmetry of adistribution by visual inspection, and as a graphical tool for comparing the distribution of severalgroups. It is useful to display Figure 3.5 on page 118 that indicates the shape of the boxplot for fourdifferent distributions. Then, use PHStat or Minitab to construct a boxplot. Note that you canconstruct the boxplot for a single group or for multiple groups.If you desire, you can discuss descriptive measures for a population and introduce theempirical rule and the Chebyshev rule.If time permits, and you have covered scatter plots in Chapter 2, you can briefly discuss thecovariance and the coefficient of correlation as a measure of the strength of the association betweentwo numerical variables. Point out that the coefficient of correlation has the advantage as compared tothe covariance of being on a scale that goes from -1 to +1. Figure 3.8 on p. 127 is useful in depictingscatter plots for different coefficients of correlation.Once again, you will find that the chapter review problems provide large data sets withnumerous variables.TheManaging Ashland MultiComm Servicescase enables students to examine the use ofdescriptive statistics in an actual business environment. The Digital case continues the evaluation ofthe EndRun Financial Services discussed in the Digital case in Chapter 2. TheCardioGood Fitnesscase focuses on developing a customer profile for a market research team.More Descriptive ChoicesFollow-upexpands on the discussion of the mutual funds data. TheClear Mountain State StudentSurveyprovides data collected from a sample of undergraduate students and a separate sample ofgraduate students.The Excel Guide for the chapter includes instructions on using different Excel functions tocompute various statistics. Alternatively, you can use PHStat or the Analysis ToolPak to compute alist of statistics. PHStat can be used to construct a boxplot.

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Teaching Tips12Chapter 4The chapter on probability represents a bridge between the descriptive statistics alreadycovered and the topics of statistical inference, regression, time series, and quality improvement to becovered in subsequent chapters. In many traditional statistics courses, often a great deal of time isspent on probability topics that are of little direct applicability in basic statistics. The approach in thistext 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 bemore 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, withan example that relates to a business application shown as a two-way contingency table (see theUsing Statistics example). If desired, you can use In-Depth Excel or PHStat to compute probabilitiesfrom 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. TheThink about Thisconcerning emailSPAM 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 binomialdistribution will be covered in Chapter 5.Be aware that in a one-semester course where time is particularly limited, these topics may beof marginal importance. The Digital case in this chapter extends the evaluation of the EndRunFinancial Services to consider claims made about various probabilities. TheCardioGood Fitness,More Descriptive Choices Follow-up, andClear Mountain State Student Surveyeach involvedeveloping contingency tables to be able to compute and interpret conditional and marginalprobabilities.

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Teaching Tips13Chapter 5Now that the basic principles of probability have been discussed, the probability distributionis developed and the expected value and variance (and standard deviation) are computed andinterpreted. Given that a probability distribution has been defined, you can now discuss some specificdistributions. Although every introductory course undoubtedly covers the normal distribution to bediscussed in Chapter 6, the decision about whether to cover the binomial or Poisson distributions ismatter 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 formulais to follow the Using Statistics example that involves an accounting information system. Note, in thisexample, the value forpis 0.10. (It is best not to use an example withp= 0.50 since this represents aspecial case). The discussion proceeds by asking how you could get three tagged order forms in asample of 4. Usually a response will be elicited that provides three items of interest out of fourselections in a particular order such as Tagged Tagged Not Tagged Tagged. Ask the class, whatwould be the probability of getting Tagged on the first selection? When someone responds 0.1, askthem how they found that answer and what would be the probability of getting Tagged on the secondselection. 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 thethird selection and the students respond 0.9, point out that this is a second assumption of the binomialdistribution -- that only two outcomes are possible -- in this case Tagged and Not Tagged, and thesum of the probabilities of Tagged and Not Tagged must add to 1.0. Now you can compute theprobability of three out of four in this order by multiplying (0.1)(0.1)(0.9)(0.1) to get 0.0036. Ask theclass if this is the answer to the original question. Point out that this is just one way of getting threeTagged out of four selections in a specific order, and, that there are four ways to get three Tagged outof four selections This leads to the development of the binomial formula Equation (5.5). You mightwant to do another example at this point that calls for adding several probabilities such as three ormore Tagged, less than three Tagged, etc. Complete the discussion of the binomial distribution withthe computation of the mean and standard deviation of the distribution. Be sure to point out that forsamples greater than five, computations can become unwieldy and the student should use PHStat, anExcel function, the binomial tables (See the OnlineBinomial.pdftables) or Minitab.If you cover the Poisson distribution, point out the distinction between the binomial andPoisson distributions. Note that the Poisson is based on an area of opportunity in which you arecounting occurrences within an area such as time or space. Contrast this with the binomialdistribution in which each value is classified as of interest or not of interest. Point out the equations

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