Statistics for Managers Using Microsoft Excel 8th Edition Solution Manual

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Table of ContentsTeaching Tips...................................................................................................................................1Chapter 1Defining and Collecting Data...............................................................................................39Chapter 2Organizing and VisualizingVariables.................................................................................46Chapter 3Numerical Descriptive Measures.......................................................................................141Chapter 4Basic Probability................................................................................................................183Chapter 5Discrete Probability Distributions......................................................................................190Chapter 6The Normal Distribution and Other Continuous Distributions..........................................215Chapter 7Sampling Distributions.......................................................................................................241Chapter 8Confidence Interval Estimation..........................................................................................261Chapter 9Fundamentals of Hypothesis Testing: One-Sample Tests..................................................292Chapter 10Two-Sample Tests.............................................................................................................337Chapter 11Analysis of Variance..........................................................................................................415Chapter 12Chi-Square and Nonparametric Tests................................................................................441Chapter 13Simple Linear Regression..................................................................................................482Chapter 14Introduction to Multiple Regression..................................................................................521Chapter 15Multiple Regression Model Building.................................................................................584Chapter 16Time-Series Forecasting.....................................................................................................641Chapter 17Getting Ready to Analyze Data in the Future....................................................................696Chapter 18Statistical Applications in Quality Management (Online).................................................748Chapter 19Decision Making (Online)..................................................................................................781Online Sections..................................................................................................................820Instructional Tips and Solutions for Digital Cases.............................................................883TheBrynne PackagingCase..............................................................................................918TheCardioGood FitnessCase...........................................................................................920

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TheChoice Is Yours/More Descriptive Choices Follow-upCase....................................1043TheClear Mountain State Student SurveysCase.............................................................1130TheCraybill Instrumentation CompanyCase..................................................................1230TheManaging Ashland MultiComm ServicesCase.........................................................1232TheMountain States Potato CompanyCase....................................................................1287TheSure Value Convenience StoresCase........................................................................1296

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PrefaceThe first part of theInstructor’s Solutions Manualcontains our educational philosophy and teaching tipsfor each chapter of the text. Solutions to End-of-Section Problems and Chapter Review Problems in eachchapter follow.Instructional tips and solutions for the digital casesare included next.Answers to theBrynne PackagingCase, theCardioGood FitnessCase, theChoice Is Yours/More Descriptive ChoicesFollow-up Case, theClear Mountain State StudentSurveys Case,theCraybill Instrumentation CompanyCase, theManaging Ashland MultiComm ServicesCase, theMountain States Potato Company CaseandtheSure Value Convenience StoresCase are included last.The purpose of thisInstructor’s Solutions Manualis to facilitate grading of assignments or exams byinstructors and/or teaching assistants. Screen shots using output from PHStat are integrated throughout.Most of the problems are solved using PHStat. To present the steps involved in solving a problem, someintermediate numerical results are presented accurate to only a reasonable number of significant digits.Hence, instructors are reminded that the final results presented in this manual that are obtained usingPHStat can sometimes be different from those obtained with a hand calculator computed using theintermediate values due to rounding.

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Teaching Tips forStatistics for Managers using Microsoft®Excel8thEdition,GlobalEditionOur 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 newfields of studies, 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 otherdisciplines. And, in a reprise of something that occurred a generation ago, new fields of study,this time with names 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 themore critical. These new fields of study all share statistics as a foundation for further learning.We are accustomed to thinking about change, as seeking ways to continuously improve theteaching of business statistics have always guided our efforts. We actively participate in DecisionSciences Institute (DSI), American Statistical Association (ASA), and Making Statistics MoreEffective in Schools and Business (MSMESB) conferences. We use the ASA’s Guidelines forAssessment and Instruction (GAISE) reports and combine them with our experiences teachingbusiness 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 ofchange. As an author team, we bring a unique collection of experiences that we believe helps usfind the proper perspective in balancing the old and the new. Our lead author, David M. Levine,was the first educator, along with Mark L. Berenson, to create a business statistics textbook that

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discussed using statistical software and incorporated “computer output” as illustrations—just thefirst of many teaching and curricular innovations in his many years of teaching business statistics.Our second author, David F. Stephan, developed courses and teaching methods in computerinformation systems and digital media during the information revolution, creating, and thenteaching in, one of the first personal computerclassroomsin a large school of business along theway. Early in his career, he introduced spreadsheet applications to a business statistics facultyaudience that included David Levine, an introduction that would eventually led to the first editionof this textbook. Our newest co-author, Kathryn A. Szabat, has provided statistical advice tovarious business and non-business communities. Her background in statistics and operationsresearch and her experiences interacting with professionals in practice have guided her, asdepartmental chair, in developing a new, interdisciplinary academic department, BusinessSystems and Analytics, in response to the technology-and data-driven changes in business today.All three of us benefit from our many years teaching undergraduate business subjects and thediversity of interests and efforts of our past co-authors, Mark Berenson and Timothy Krehbiel.Two of us (Stephan and Szabat) also benefit from formal training and background in educationalmethods and instructional design.Educational PhilosophyAs in prior editions ofStatistics for Managers Using Microsoft Excel, we are guided by thesekey learning principles: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 aframe of reference when learning statistics, especially when statistics is not their major. Thatframe of reference for business students should be the functional areas of business, such asaccounting, finance, information systems, management, and marketing. Each statistics topic

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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 ofresults, the evaluation of the assumptions, and the discussion of what should be done if theassumptions are violated.2.Emphasize interpretation of statistical results over mathematical computation.Introductory business statistics courses should recognize the growing need tointerpretstatistical results that computerized processes create. This makes the interpretation of resultsmore important than knowing how to execute the tedious hand calculations required toproduce 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 muchas possible. Students should work with data sets, both small and large, and be encouraged tolook beyond the statistical analysis of data to the interpretation of results in a managerialcontext.4.Familiarize students with how to use statistical software to assist business decision-making.Introductory business statistics courses should recognize that programs withstatistical functions are commonly found on a business decision maker’s desktop computer.Integrating statistical softwareinto all aspects of an introductory statistics course allows thecourse to focus on interpretation of results instead of computations (see point 2).5.Provide clear instructions to students for using statistical applications.Books shouldexplain clearly how to use programs such as Microsoft Excel with the study of statistics,without having those instructions dominate the book or distract from the learning of statisticalconcepts.

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FirstThings FirstIn a time of change, you can never know exactly what knowledge and background students bringinto an introductory business statistics classroom. Add that to the need to curb the fear factorabout learning statistics that so many students begin with, and there’s a lot to cover even beforeyou teach your first statistical concept.We created“FirstThings First” to meet this challenge. This unit sets the context forexplaining what statistics is (not what students may think!) while ensuring that all students sharean understanding of the forces that make learning business statistics critically important today.Especially designed for instructors teaching with course management tools, including thoseteaching hybrid or online courses,“FirstThings First”has been developed to be posted online orotherwise distributed before the first class section begins and is available from the download pagefor this book that is discussed in Appendix Section C.1.We would argue that the most important class is the first class. First impressions are criticallyimportant. You have the opportunity toset the tone to create a new impression that the course willbe important to their business education.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 businessproblem. This approach goes across all the topics in the book and most importantly can be used asa framework in real world situations when students graduate. The approach has the acronymDCOVA, which stands 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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•Visualize the data by developing charts•Analyze the data by using statistical methods to reach conclusions.To this, you can addCfor Communicate which is critically importantYou 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 definevariable, data, and statistics.Just as computers are used not just in the computer course, students need to know thatstatistics is used not just in the statistics course.This leads you to a discussion of businessanalytics in which data is used to make decisions. Make the point thatanalyticsshould be part ofthe competitive strategy of every organizationespecially since “big data” meaning data collectedin huge volumes at very fastrates.needsto be analyzed.Inform the students that there is an Excel Guide at the end of each chapter. Stronglyencourage or require students to read the Excel Guide at the end of this chapter so that they willbe ready to use Excel with this book.

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Chapter 1You need tocontinue thediscussion of the Define task byestablishing thetypes ofvariables.Be sure to discuss the different types carefully since the ability to distinguish betweencategorical and numerical data will be crucial later in thecourse. Go over examples of each typeof variable and have students provide examples of each type.Then, if you wish, you can cover thedifferent measurement scales.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 couldspend some time discussing sampling,youmay want to take a bit more time anddiscuss the types of survey sampling methods and issues involved with survey sampling results.TheConsiderThisessay discusses the important issue of the use of Web-based surveys.The chapter also introducestwocontinuing casesrelated toManagingAshlandMultiComm ServicesandCardioGood Fitnessthat appear at the end of many chapters.TheDigitalcases are introduced in this chapter also. In these cases, students visit Web sitesrelated to companies and issues raised in the Using Statistics scenarios that start eachchapter. The goal of theDigitalcases is for students to develop skills neededto identifymisuses of statistical information. As would be the situation with manyreal world cases,inDigitalcases,students often need to sift through claims and assorted information inorder to discover the data most relevant to a case task. They will then have to examinewhether the conclusions and claims are supported by the data. (Instructional tips for usingtheManagingAshland MultiComm ServicesandDigitalcases and solutions to theManagingAshland MultiComm ServicesandDigital cases are included in thisInstructor’sSolutions Manual.).Make sure that students read the Excel Guide at the end ofeachchapter.Ways ofWorking With Excel on pages 7 and 8explains the different type of Excel instructions.TheWorkbookinstructions provide step-by-step instructions and live worksheets thatautomatically update when data changes. ThePHStat2add-ininstructions provideinstructions for using the PHStat2 add-in.Analysis ToolPakinstructions provideinstructions for using the Analysis ToolPak, the Excel add-in packagethat is includedwith many versions of Excel.

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Chapter 2This chapter moves on to the organizing and visualizing steps of the DCOVAframework. If you are going to collect sample data to use inChapters2 and 3, you canillustratesampling by conducting a survey of students in your class.Ask each student tocollect his or her own personal data concerning the time it takes to get ready to go to classin the morning or the time it takes to get to school or home from school. First, ask thestudents to write down a definition of how they plan to measure this time. Then, collectthe various answers and read them to the class. Then, a single definition could beprovided (such as the time to get ready is the time measured from when you get out ofbed 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 samplesize) in class when Chapters 2 and 3 are discussed.Then, move on to the Organize step that involves setting up your data in an Excelworksheet and develop tables to help you prepare charts and analyze your data. Beginyour discussion for categorical data with the example on p.34concerninghow peoplepay for purchases and other transactions. Show the summary table and then if you wish,explain that you can sometimes organize the data into a two-way table that has onevariable in the row and another in the column.Continue with organizing data (but now for numerical data) by referring to thecost of a restaurant meal on p.38. Show the simple ordered array and how a frequencydistribution, percentage distribution, or cumulative distributioncan summarize the rawdata in a way that is more useful.Now you are ready to tackle the Visualize step.A good way of starting thispart ofthechapter is to display the following quote."A picture is worth a thousand words."Students will almost certainly be familiar with Microsoft®Word andmayhave already usedExcel to construct charts that they have pasted into Word documents.Now you will be usingExcel to construct many different types of charts.Return to thepurchase paymentdata previouslydiscussed and illustrate how a bar chart,pie, and doughnutchart can be constructedusing Excel.Mention the advantages and disadvantagesof each chart. A good example is to show the data on

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incomplete ATM transactions on p.49and how the Pareto chart enables you to focus on the vitalfew 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 datapreviously mentioned, the retirement funds data, ordata that you have collected from your class.You may want to begin with a simple stem-and-leaf display that both organizes the data andshows a bar type chart. Then move on to the histogram and the various polygons, pointing out theadvantages and disadvantages of each.If 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.If you cover the timeseries plot, you might also want to mention sparklines that are discussed in Section 2.6.Also,if possible,you may want to discuss how multidimensional tables allow you to drilldown to individual cells of the table. You can follow this with further discussion of PivotTablesand Excel slicers that enable you to see panels for each variable being studied.If the opportunity is available, we believe that it is worth the time to cover Section 2.7onChallenges inOrganizing andVisualizingVariables. This is a topic that students very much enjoysince it allows for a great deal of classroom interaction. After discussing the fundamentalprinciples ofgoodgraphs, try to illustrate some of the improper displays shown in Figures 2.26–2.28. Ask students what is “bad” about these figures. Follow up with a homework assignmentinvolving Problems 2.69–2.73(USA Todayis a great source).You will find that the chapter review problems provide large data sets with numerousvariables. Report writing exercisesprovide the opportunity for students to integrate written and ororal presentation with the statistics they have learned.TheManagingAshland MultiComm Servicescase enables students to examine the use ofstatistics in an actual business environment.TheDigital caserefers to theEndRunFinancialServicesand claims that have been made.The CardioGood Fitness case focuses on developing acustomer profile for a market research team. The Choice Is Yours Follow-up expands on thechapter discussion of the mutual funds data. The Clear Mountain State Student Survey providesdata collected from a sample of undergraduate students.The Excel Guide for this and the remaining chaptersareorganized according to thesections of the chapter. It is quite extensive since it covers both organizing and visualizing manydifferent graphs.The Excel Guideincludes instructions forWorkbook, PHStat2, and the AnalysisToolPak.

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Chapter 3This chapter ondescriptivenumerical statisticalmeasures represents the initialpresentation of statistical symbols in the text. Students who need to review arithmetic andalgebraic conceptsmay wish to refer to AppendixA for a quick review or to appropriate texts(seewww.pearson.com) or videos (www.videoaidedinstruction.com). Once again, as with thetables and chartsconstructed fornumericaldata, it is useful to provide an interesting set of datafor classroomdiscussion.If a sample of students was selected earlier in the semester and dataconcerning student time to get ready or commuting time was collected (see Chapters 1 and 2), usethese data in developing the numerous descriptive summary measures in this chapter. (If theyhave not been developed,useother data for classroom illustration.)Discussion of the chapter begins with the property of central tendency. We have foundthat 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 themeanforyour classroom example. Emphasize the effect of extreme values on the arithmetic mean andpoint out that themeanis like the center of a seesaw--a balance point. Note that you will returnto this concept later when you discuss the variance and the standard deviation. You might want tointroduce summation notation at this point and express the arithmetic mean in formula notation asin Equation (3.1). (Alternatively, you could wait until you cover the variance and standarddeviation.) A classroom example in which summation notation is reviewed is usually worthwhile.Remind the studentsagainthat Appendix Aincludesa review of arithmetic and algebra andsummation 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 themedian 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 tellsus something about another property of data (skewness). Following the median, the mode can bebriefly discussed. Once again, have the students compare this result to those of the arithmeticmean and median for your data set.If time permits, you can also discuss the geometric meanwhich is heavily used in finance.The completion of the discussion of central tendencyleadsto the second characteristic ofdata, variability. Mention that all measures of variation have several things in common: (1) theycan never be negative, (2) they will be equal to 0 when all items are the same, (3) they will besmall when there isn't much variation, and (4) they will be large when there isagreat deal ofvariation.

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The first measure of variability to consider is the simplest one, the range. Be sure to pointout that the range only provides information about the extremes, not about the distributionbetween the extremes.Point out thatthe rangelacksone important ingredient, the ability to takeinto account each data value. Bring up the idea of computing the differences around the mean, butthen return to the fact that as the balance point of the seesaw, these differences add up to zero. Atthat point, ask the students whattheycan do mathematically to remove the negative sign for someof the values. Most likely, they will answer by telling you to square them (although someonemay realize that the absolute value could be taken). Next, you may want to define the squareddifferences as a sum of squares. Now you need to have the students realize that the number ofvalues being considered affects the magnitude of the sum of squared differences. Therefore, itmakes sense to divide by the number ofvalues andcomputea measure called the variance. If apopulation is involved, you divide byN, the population size, but if you are using a sample, youdivide byn-1, to make the sample result a better estimate of the population variance. You canfinish the development of variation by noting that since the variance is in squared units, you needto take the square root tocompute the standard deviation.Anothermeasure of variation that can be discussed is the coefficient of variation. Be sureto illustrate the usefulness of this as a measure of relative variation by using an example in whichtwo data sets have vastly different standard deviations, but also vastly different means. A goodexample is one that involves the volatility of stock prices. Point out that the variation of the priceshould be considered in the context of the magnitude of the arithmetic mean.The final measure ofvariation is theZscore. Point out that this provides a measure of variation in standard deviationunits. You can also say that you will return toZscores in Chapter 6 when the normal distributionwill 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 andmedian.You may also want to briefly mention the property of kurtosis which is the relativeconcentration of values in the center of the distribution as compared to the tails.Thisstatistic isprovided by Excel through an Excel function or theAnalysis Toolpak.Once these three characteristics have been discussed, you are ready to show how they canbe computed using Excel.Now that these measuresare understood, you can further explore data by computing thequartiles, the interquartile range, the five number summary, and constructing a boxplot.Youbegin bydeterminingthe quartiles. Reference here can be made to the standardized exams thatstudents have taken, and the quantile scores that they have received (97th percentile, 48th

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percentile, 12thpercentile,etc.). Explain that the1stand 3rdquartiles are merely two specialquantiles--the 25th and 75th, that unlike the median(the 2ndquartile), are not at the center of thedistribution.Once thequartiles havebeen computed, the interquartile range can be determined.Mentionthat the interquartile range computes the variation in the center of the distribution ascompared to the difference in theextremes computed by the range.You can thendiscussthe five-number summary of minimum value, first quartile, median,third quartile, and maximum value. Then, you construct theboxplot. 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. Itisuseful to display Figure 3.6on page118that indicates the shape of the boxplot forfour different distributions. Then, use PHStat2 toconstructa boxplot. Note thatyou can constructtheboxplot for a single group or for multiple groups.If you desire, you can discuss descriptive measures for a population and introduce theempirical rule and theChebyshevrule.If time permits, and you have covered scatterplots in Chapter 2, you can briefly discussthecovariance and thecoefficient of correlation as a measure of the strength of the associationbetween two numerical variables.Point out that the coefficient of correlation has the advantage ascompared to the covariance of being on a scale that goes from-1 to +1.Figure 3.9on p.127isuseful in depicting scatterplots for different coefficients of correlation.Once again, you will find that the chapter review problems provide large data sets withnumerous variables.TheManagingAshland MultiComm Servicescase enables students to examine the use ofdescriptive statistics in an actual business environment. TheDigital casecontinues the evaluationof theEndRunFinancialServicesdiscussed in theDigital casein Chapter 2.The CardioGoodFitness case focuses on developing a customer profile for a market research team. MoreDescriptiveChoices Follow-up expands on the discussion of the mutual funds data. The ClearMountain State Student Survey provides data collected from a sample of undergraduate students.The Excel Guide for the chapter includes instructions on using different Excel functionsto compute various statistics. Alternatively, you can usePHStat orthe Analysis ToolPak tocompute a list of statistics.PHStat2 can be used to construct a boxplot.

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Chapter 4The chapter on probability represents a bridge between the descriptive statistics alreadycovered and the topics of statistical inference, regression, time series, andbusiness analyticsto 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 inthis 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) noprobability can be more than 1, and (3) the sum of the probabilities of a set of mutually exclusiveevents adds to 1.0. Students often understand the subject best if it is taught intuitively with aminimum of formulas, with an example that relates to a business application shown as a two-waycontingency table (see the Using Statistics example). If desired,you can usethe ExcelWorkbookinstructionsorPHStat2 to compute probabilities from the contingency table.Once these basic elements of probability have been discussed, if there is time and youdesire, conditional probability and Bayes’theorem(an online topic)can be covered.TheConsiderThisconcerning email SPAM is a wonderful way of helping studentsrealize theapplication of probability to everyday life.Be aware that in a one-semester course where time isparticularly limited, these topics may be of marginal importance.TheDigital casein this chapterextends the evaluation of theEndRunFinancialServicesto consider claims made about variousprobabilities.The CardioGood Fitness, MoreDescriptiveChoices Follow-up, and Clear MountainState Student Survey each involve developing contingency tables to be able to compute andinterpret conditional and marginal probabilities.

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Chapter 5Now that the basic principles of probability have been discussed, the probabilitydistribution is developed and the expected value and variance (and standard deviation) arecomputed and interpreted. Given that a probability distribution has been defined, you can nowdiscuss some specific distributions. Although every introductory course undoubtedly covers thenormal distribution to be discussed in Chapter 6, the decision about whether to cover thebinomial, Poisson, or hypergeometric distributions is matter of personal choice and depends onwhether the course is part of a two-course sequence.If the binomial distribution is covered, an interesting way of developing the binomialformula is to follow the Using Statistics example that involves an accounting information system.Note, in this example, the value forpis 0.10. (It is best not to use an example withp= 0.50 sincethis represents a special case). The discussion proceeds by asking how you could get three taggedorder forms in a sample of 4. Usually a response will be elicited that provides threeitems ofinterestout of four selections in a particular order such as Tagged Tagged Not Tagged Tagged.Ask the class, what would be the probability ofgetting Tagged on the first selection? Whensomeone responds 0.1, ask them how theyfoundthat answer and what would be the probabilityof getting Tagged on the second selection. When they answer 0.1 again, you will be able to makethe point that in saying 0.1 again, they are assuming that the probability of Tagged stays constantfrom trial to trial. When you get to the third selection and the students respond 0.9, point out thatthis 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 Taggedmust add to 1.0. Now you can compute the probability of three out of four inthisorder bymultiplying (0.1)(0.1)(0.9)(0.1) to get 0.0009. Ask the class if this is the answer to the originalquestion. Point out that this is just one way of getting three Tagged out of four selections in aspecific order, and, that thereare four ways to getthree Tagged out of four selections.Thisleadsto thedevelopment of the binomial formula Equation (5.5). You might want to do anotherexample at this point that calls for adding several probabilities such as three or more Tagged, lessthan three Tagged, etc. Complete the discussion of the binomial distribution with the computationof the mean and standard deviation of the distribution. Be sure to point out that for samplesgreater than five, computations can become unwieldy and the student should use PHStat2,anExcelfunction,or the binomial tables (See the OnlineBinomial.pdftables).Once the binomial distribution has beencovered,if time permits, other discreteprobabilitydistributions can be presented. If you cover the Poisson distribution, pointoutthedistinction between the binomial and Poisson distributions. Note that the Poisson is based on an

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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 asof interestornotof interest. Point out the equations for the mean and standard deviation of the Poisson distributionandindicatethat the mean is equal to the variance.Since the computation of probabilities fromthese discrete probability distributions can become tedious for other than small sample sizes, it isimportant to discuss PHStat2,anExcel functionor the Poisson tables (See the OnlinePoisson.pdftables).If you so desire, you candiscuss the covarianceof a probability distribution (onlineSection 5.4), which is of particular importance to students majoring in finance. It is referred to invarious finance courses including those on portfolio management and corporate finance. Use theexample in the text to illustrate the covariance. If desired, continue with coverage of portfolioexpected return and portfolio risk. Note that the PHStat2Covariance and Portfolio Managementmenu selection allows you to readily compute the pertinent statistics. It also allows you todemonstrate changes in either the probabilities or the returns and their effect on the results.If youare using Workbook, you can start with the Portfolio.xls workbook and show how various Excelfunctions can be used to compute the desired statistics.The hypergeometric distribution(online Section 5.5)can be developed for the situation inwhich one is sampling without replacement. Once again, use PHStat2or an Excelfunction.TheManagingAshland MultiComm Servicescase for this chapter relates to the binomialdistribution. TheDigital caseinvolves the expected value and standard deviation of a probabilitydistribution and applications of the covariance in finance.

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Chapter 6Now that probability and probability distributions have been discussed in Chapters4and5, you are ready to introduce the normal distribution. We recommend that you begin bymentioning some reasons that the normal distribution is so important and discuss several of itsproperties. We would also recommend that you do not show Equation (6.1) in class as it will justintimidate some students. You might begin by focusing on the fact that any normal distribution isdefined by its mean and standard deviation and display Figure 6.3 on p.193. Then, an examplecan be introduced and you can explain that if you subtracted the mean from a particular value,and divided by the standard deviation, the difference between the value and the mean would beexpressed as a standardizednormalorZscorethat was discussed in Chapter 3.Next, use TableE.2, the cumulative normal distribution, to find probabilities under the normal curve. In the text,the cumulative normal distribution is used since this table is consistent with results provided byExcel.Make sure that all the students can find the appropriate area under the normal curve intheir cumulative normal distribution tables. If anyone cannot, show them how to find the correctvalue. Be sure to remind the class that since the total area under the curve adds to 1.0, the wordarea is synonymous with the word probability. Once this has been accomplished, a good approachis to work through a series of examples with the class, having a different student explain how tofindeach answer. The example that will undoubtedly cause the mostdifficultywill be finding thevalues corresponding to known probabilities. Slowly go over the fact that in this type of example,the probability is known and theZvalue needs to bedetermined, which is the opposite of whatthe student has done in previous examples. Also point out that in cases in which the unknownXvalue is below the mean, the negative sign must be assigned to theZvalue. Once the normaldistribution has been covered, youcanuse PHStat2,orvarious Excel functionstocomputenormal probabilities.You can alsouse the Visual Explorationsin StatisticsNormal distributionprocedureon p.199. This will be useful if you intend to use examples that explore the effect onthe probabilities obtained by changing theXvalue, the population mean,, or the standarddeviation,.TheConsiderThisessay provides a historical perspective of the application of thenormal distribution.If you have sufficient time in the course, the normal probability plot can be discussed. Besure to note that all thedata values need to be ranked in order from lowest to highest and thateach value needs to be converted to a normal score. Again,you can eitheruse PHStat2togenerate a normal probability plotor use Excel functions andcharts.If time permits, you may want to cover the uniform distribution and referto the table ofrandom numbers as an example of this distribution. If you plan to cover the exponential

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distribution(which is an online topic), it is useful to discuss applications of this distribution inqueuing(waiting line) theory. In addition, be sure to point out that Equation (6.10) provides theprobability of an arrival in less than or equal to a given amount of time. Be sure to mention thatyou can usePHStat2oranExcel functiontocomputeexponential probabilities.TheManagingAshland MultiComm Servicescase for this chapter relates to the normaldistribution. TheDigital caseinvolves the normal distribution and the normal probability plot.The CardioGood Fitness, MoreDescriptiveChoices Follow-up, and Clear Mountain StateStudent Survey each involve developingnormal probability plots.You can use either Excel functions or the PHStat add-in to compute normal andexponential probabilities and to construct normal probability plots.

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Chapter 7The coverage of the normal distributionin Chapter 6flows into a discussion of samplingdistributions. Point out the fact that the concept of the sampling distribution of a statistic isimportant for statistical inference. Make sure that students realize that problems in this sectionwillcomputeprobabilities concerning the mean,not concerning individual values. It is helpful todisplay Figure7.4on p.224to show how the Central Limit Theorem applies to different shapedpopulations. A useful classroom or homework exercise involves using PHStat2or Exceltoformsampling distributions. This reinforces the concept of the Central Limit Theorem.TheManagingAshland MultiComm Servicescase for this chapter relates to the samplingdistribution of the mean. TheDigital casealsoinvolves the sampling distribution of the mean.You might want to have students experiment with using the Visual Explorations add-inworkbook to explore sampling distributions. You can also use either Excel functions, the PHStatadd-in, or the Analysis ToolPak to develop sampling distribution simulations.

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Chapter8You should begin this chapter by reviewing the concept of the sampling distributioncovered in Chapter7. It is important that the students realize that (1) an interval estimate providesa range of values for the estimate of the population parameter, (2) you can never be sure that theinterval developed does include the population parameter, and (3) the proportion of intervals thatinclude the population parameter within the interval is equal to the confidence level.Note that the Using Statistics example for this chapter, which refers to theRicknel HomeCentersis actuallya case study that relates to every part of the chapter. Thisscenariois a goodcandidate for use as the classroom example demonstrating an application of statistics inaccounting.It also enables you to use the DCOVA approach of Define, Collect,Organize,Visualize, and Analyze in the context of statistical inference.When introducing thetdistribution for the confidence interval estimate of the populationmean, be sure to point out the differences between thetand normal distributions, the assumptionof normality, and the robustness of the procedure. It is useful to display Table E.3 in class toillustrate how to find the criticaltvalue. When developing the confidence interval for theproportion, remind the students that the normal distribution may be used here as anapproximation to the binomial distribution as long as the assumption of normality is valid [whennandn(1-) are at least 5].Having covered confidence intervals, you can move on to sample size determination byturning the initial question of estimation around, and focusing on the sample size needed for adesired confidence level and width of theinterval. In discussing sample size determination for themean, be sure to focus on the need for an estimate of the standard deviation. When discussingsample size determination for the proportion, be sure to focus on the need for an estimate of thepopulation proportion and the fact that a value of= 0.5 can be used in the absence of any otherestimate. If time permits, you may wish to discuss the effect of the finite population (thisisanOnline Topic) on the width of the confidence interval and the sample size needed. Point out thatthe correction factor should always be used when dealing with a finite population, but will haveonly a small effect when the sample size is a small proportion of the population size.Due to the existence of a large number of accounting majors in many business schools,we have included an onlinesection on applications of estimation in auditing. Two applicationsare included, the estimation of the total, and difference estimation. In estimating the total, pointout that estimating the total is similar to estimating the mean, except that you are multiplying boththe mean and the width of the confidence interval by the population size. When discussingdifference estimation, be sure that the students realize that all differences of zero must be

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accounted for in computing themeandifference and the standard deviation of the differencewhenusing Equations (8.8) and (8.9).Since the formulas for the confidence interval estimates and sample sizes discussed inthis chapter are straightforward, using PHStat2orWorkbookcan remove much of the tediousnature of these computations.TheManagingAshland MultiComm Servicescase for this chapter involvesdevelopingvarious confidence intervals and interpreting the results in a marketing context. TheDigital casealso relates to confidence interval estimation.This chapter marks the first appearance of the SureValue Convenience Store case which places the student in the role of someone working in thecorporate office of a nationwide convenience store franchise. This case will appear in the nextthree chapters, Chapters 9–12, and also in Chapter 15.The CardioGood Fitness, MoreDescriptiveChoices Follow-up, and Clear Mountain State Student Survey each involvedeveloping confidence interval estimates.You can use either Excel functions or the PHStat add-in to construct confidence intervalsfor means and proportions and to determinethesample size for means and proportions.

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Chapter9A good way to begin the chapter is to focus on the reasons that hypothesis testing is used.We believe that it is important for students to understand the logic of hypothesis testing beforethey delve into the details of computing test statistics and making decisions. If you begin with theUsing Statistics example concerning the filling of cereal boxes, slowly develop the rationale forthe null and alternative hypotheses. Ask the students what conclusion they would reach if asample revealed ameanof 200 grams (They will all say that something iswrong) and if a samplerevealed ameanof 367.99 grams (Almost all will say that the difference between the sampleresult and what themeanis supposed to be is so small that it must be due to chance). Be sure tomake the point that hypothesis testing allows you to take away the decision from a person'ssubjective judgment, and enables you to make a decision while at the same time quantifying therisks of different types of incorrect decisions. Be sure to go over the meaning of the Type I andType II errors, and their associated probabilitiesandalong with the concept of statisticalpower (more extensive coverage of the power ofatest is included in Section9.6which is anOnline Topic).Set up an example of a sampling distribution such as Figure9.1on p.273, and show theregions of rejection and nonrejection. Explain that the sampling distribution and the test statisticinvolved will change depending on the characteristic being tested.Focus on the situation whereis unknown if you have numerical data. Emphasize thatis virtuallynever known.It is alsouseful at this point to introduce the concept of thep-value approach as an alternative to theclassicalhypothesis testing approach. Define thep-valueand use thephrasegiven in the text “Ifthep-value is low,Homust go.”and the rules for rejecting the null hypothesis and indicate thatthep-value approach is a natural approach when using Excel, since thep-value can bedeterminedby using PHStat, Excel functions,ortheAnalysis Toolpak.Once the initial example of hypothesis testing has been developed, you need to focus onthe differences between the tests used in various situations. The Chapter9summarytableisuseful for this since it presents aroad map for determining which test is used in whichcircumstance. Be sure to point out that one-tailtests are used when the alternative hypothesisinvolved is directional (e.g.,> 368,<0.20). Examine the effect on the results of changing thehypothesized mean or proportion.TheManagingAshland MultiComm Servicescase,Digital case, and the Sure ValueConvenience Store case eachinvolvesthe use of the one-sample testof hypothesis for the mean.

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You can use either Excel functions or the PHStat add-in to carry out the hypothesis testsfor means and proportions.

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Chapter10This chapter discusses tests of hypothesis for the differences between two groups. Thechapter begins withttests for the difference between the means, then covers theZtest for thedifference between two proportions, and concludes with theFtest for theratio oftwo variances.The first test of hypothesis covered is usually the test for the difference between themeans of two groups for independent samples. Point out that the test statistic involves pooling ofthe sample variances from the two groups and assumes that the population variances are the samefor the two groups. Students should be familiar with thetdistribution, assuming that theconfidence interval estimate for the meanhas been previously covered,Point out that a stem-and-leaf display, a boxplot, or a normal probability plot can be used to evaluate the validity of theassumptions of thettest for a given set of data.This allows you to once again use the DCOVAapproach of Define, Collect,Organize, Visualize, and Analyze to meet a business objective.Once thettest has been discussed,you can use the Excel worksheets provided with theWorkbookapproach, PHStat2,ortheAnalysis Toolpaktodeterminethe test statistic andp-value.Mention that if the variances are not equal, a separate variancettest can beconducted.TheConsiderThisessay is a wonderful example of how the two-samplettest was used to solve abusiness problem that a student had after she graduated and had taken the introductory statisticscourse.At this point, having covered the test for the difference between the means of twoindependent groups,if you have time in your course,you can discuss a test thatexaminesdifferences in the means of two paired or matched groups. The key difference is that the focus inthis test is on differences between thevalues in the two groups since the data have been collectedfrom matched pairs or repeated measurements on the same individuals or items. Once the pairedttest has been discussed, theWorkbookapproach, PHStat2,orthe Data Analysis tool can be usedtodeterminethe test statistic andp-value.You can continue the coverage of differences between two groups by testing for thedifference between two proportions. Be sure to review the difference between numerical andcategorical data emphasizing the categorical variable used here classifies each observation asofinterestornot of interest. Make sure that the students realize that the test for the differencebetween two proportions follows the normal distribution. A good classroom example involvesasking the students if they enjoy shopping for clothing and then classifying the yes and noresponses by gender. Since there willoftenbe a difference between males and females, you canthen ask the class howtogo about determining whether the results are statistically significant.

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TheF-test for thedifference between twovariances can be covered next. Be sure tocarefully explain that this distribution, unlike the normal andtdistributions, is not symmetric andcannot have a negative value since the statistic is the ratio of two variances.Remind the studentsthat the larger variance isplacedin the numerator.Be sure to mention that a boxplot of the twogroups and normal probability plots can be used to determine the validity of the assumptions oftheFtest.This is particularly important here sincethis test is sensitive to non-normality in thetwo populations.TheWorkbookapproach, PHStat2,ortheAnalysis Toolpakcan be used todeterminethe test statistic andp-value.The online section on effect size is particularly appropriate when you have big data withvery large sample sizes.BeawarethattheManagingAshland MultiComm Servicescasesince it contains bothindependent sample and matchedsample aspects,involves all the sections of the chapter exceptthe test for the difference between two proportions. TheDigital caseis based on two independentsamples. Thus, only the sections on thettest for independent samples and theFtest for thedifference between two variances are involved.The Sure Value Convenience Store case nowinvolves a decision between two prices for coffee. The CardioGood Fitness, MoreDescriptiveChoices Follow-up, and Clear Mountain State Student Survey each involve the determination ofdifferences between two groups on both numerical and categorical variables.You can use either Excel functions, thePHStat add-in, or the Analysis ToolPak to carryout the hypothesis tests for the differences between means and variances and for the pairedttest.You can also use Excel functions or the PHStat add-in to carry out the hypothesis test for thedifferences between two proportions.

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Chapter 11If the one-way ANOVAFtest for the difference betweencmeans is to be covered inyour course, a good way to start is to go back to the sum of squares concept that was originallycovered when the variance and standard deviation were introduced in Section 3.2. Explain that intheone-way Analysis of Variance, the sum of squared differences around the overall mean can bedivided into two other sums of squares that add up to the total sum of squares. One of thesemeasures differences among the means of the groups and thus is called sum of squares amonggroups (SSA), while the other measures the differences within the groups and is called the sum ofsquares within the groups (SSW). Be sure to remind the students that, since the variance is a sumof squares divided by degrees of freedom, a variance among the groups and a variance within thegroups can becomputed by dividingeachsum of squares by thecorrespondingdegrees offreedom. Make the point that the terminology used in the Analysis of Variance for variance isMean Square, so the variances computed are calledMSA,MSW, andMST. This will lead to thedevelopment of theFstatistic as the ratio of two variances. A useful approach at this point whenall formulas are defined, is to set up the ANOVA summary table. Try to minimize the focus onthe computations by reminding students that the Analysis of Variance computations can be doneusingWorkbook, PHStat2,ortheAnalysisToolpak. It is also useful to show how to obtain thecriticalFvalue by either referring to Table E.5or the Excel results. Be sure to mention theassumptions of the Analysis of Variance and thattheboxplot and normal probability plotcan beused to evaluate the validity of these assumptions for a given set of data. Levene’s test can beused to test for the equality of variances.WorkbookorPHStat2can be used to compute theresults for this test.Once the Analysis of Variance has been covered, if time permits, you will want todetermine which means are different. Although many approaches are available, this text uses theTukey-Kramer procedure that involves the Studentized range statistic shown in Table E.7. Besure that students compare each paired difference betweenthemeans to the critical range. Notethatyou can useWorkbookorPHStat2tocomputeTukey-Kramer multiple comparisons.The factorial design modelin Section 11.2provides coverage of the two-way analysis ofvariance with equal number of observations for each combination of factorAand factorB. Theapproach taken in the text is primarily conceptual since, due to thecomplexityof thecomputations, the AnalysisToolPak, orPHStat2should be used to perform the computations.You should develop the concept of partitioning the total sum of squares (SST) into factorAvariation (SSA), factorBvariation (SSB), interaction (SSAB) and random variation (SSE). Thenmove on to the development of the ANOVA table displayed in Table11.6on p.367. Perhaps the

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most difficult concept to teach in the factorial design model is that of interaction. We believe thatthe display of an interaction graph such as the one shown in Figure11.13onp.371is helpful. Inaddition, showing an example such as Example11.2on page371is particularly important, so thatstudents observe the lack of parallel lines when significant interaction is present. Be sure toemphasize that the interaction effect is always tested prior to the main effects ofAandB, sincethe interpretation of effectsAandBwill be affected by whether the interaction is significant.The randomized block model which is an online topic is an extension of the pairedttestin Chapter 10.Slowly go over the partitioning of the total sum of squares (SST) into AmongGroup variation (SSA), Among Block variation (SSBL), and Random variation (SSE). Discuss theANOVA table and be sure students realize thatExcelcan be used to perform the computations.Finish this topic with a brief discussion of the relative efficiency of using the randomized blockmodel and the use of the Tukey procedure for multiple comparisons.The online Section 11.4briefly discusses the difference between theFtests involved when there are fixed and randomeffects.TheManagingAshland MultiComm Servicescase for this chapter involves the one wayANOVA and the two-factor factorial design. TheDigital caseuses the One Way ANOVA.TheSure Value Convenience Store case now involves a decisionamongfour prices for coffee. TheCardioGood Fitness, MoreDescriptiveChoices Follow-up, and Clear Mountain State StudentSurvey each involves usingthe one-way ANOVA to determine whether differences in numericalvariables exist among three or more groupsIn this chapter, usingWorkbookis more complicated than in other chapters, so you maywant to focus on using the Analysis ToolPak or PHStat2.

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Chapter 12This chapter covers chi-square tests and nonparametric tests. The Using Statisticsexample concerning hotels relates to the first three sections of the chapter.If you covered theZtest for the difference between two proportions in Chapter10, youcan return to the example you used there and point out that the chi-square test can be used as analternative. A good classroom example involves asking the students if they enjoy shopping forclothing(or revisiting Chapter 10’s example)and then classifying the yes and no responses bygender. Since there willoftenbe a difference between males and females, you can then ask theclass howthey might go about determining whether the results are statistically significant. Theexpected frequencies arecomputed by finding themeanproportion ofitems of interest(enjoyingshopping) anditems not of interest(not enjoying shopping) and multiplying by the sample sizesof males and females respectively. This leads to the computation of the test statistic. Once againas with the case of the normal,t, andFdistribution, be sure to set up a picture of the chi-squaredistribution with its regions of rejection and non-rejection and critical values. In addition, go overthe assumptions of the chi square test including the requirement for an expected frequency of atleast five in each cell of the2 × 2contingency table.Now you are ready to extend the chi-square test to more than two groups. Be sure todiscuss the fact that with more than two groups, the number of degrees of freedom will changeand the requirements for minimum cell expected frequencies will be somewhat less restrictive. Ifyou have time, you can develop the Marascuilo procedure to determine which groups differ.The discussion of the chi-square test concludes with the test of independence in therbyctable. Be sure to go over the interpretation of the null and alternative hypotheses and how theydiffer from the situation in which there are only two rows.If you will be covering the Wilcoxon rank sum test, begin by noting that if the normalityassumption was seriously violated, this test would be a good alternative to thettest for thedifference between the means of two independent samples. Be sure to discuss the need to rank allthe data values without regard to group. Review the fact that the statisticT1refers to the sum ofthe ranks for the group with the smaller sample size. If small samples are involved, be sure topoint out that the null hypothesis is rejected if the test statisticT1is less than or equal to the lowercritical value or greater than or equal to the upper critical value. In addition, explain when thenormal approximation can be used. Point out thatWorkbookorPHStat2can be used for theWilcoxon rank sum test.

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If the Kruskal-Wallisranktest is to be covered, you can explain that if the assumption ofnormality has been seriously violated, the Kruskal-Wallisranktest may be a better test procedurethan the one-way ANOVA. Once again, be sure to discuss the need to rank all the data valueswithout regard to group. Go over how tofind thecritical values of thechi-square statistic usingTable E.4. As was the case with the Wilcoxon rank sum test,WorkbookorPHStat2can be usedfor the Kruskal-Wallisranktest.If you wish, you can briefly discuss the McNemar testwhich is an online topic. Explainthat just like you usedthe paired-ttest when you had related samples of numerical data, you usethe McNemar test instead of the chi-square test when you have related samples of categoricaldata. Make sure to state that for two samples of related categorical data, the McNemar test ismore powerful than the chi-square test.You can then move on, if you wish, to the one sample test for the variancewhich is anonline topic. Remind the students that if they are doing a two-tail test, theyalsoneed to find thelower critical value in the lower tail of the chi-square distribution.TheManagingAshland MultiComm Servicescase extends the survey discussed inChapter8to analyze data from contingency tables. TheDigital casealso involves analyzingvarious contingency tables.The Sure Value Convenience Store case and the CardioGood Fitnesscases involve using the Kruskal-Wallis test instead of the one-way ANOVA, The MoreDescriptive Choices Follow-up and Clear Mountain State Student Survey cases involve bothcontingency tables and nonparametric tests.You can useWorkbookorPHStat2.for testing differences between the proportions, testsof independence, and also for the Wilcoxon rank sum test and the Kruskal-Wallis test.

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