Solution Manual for Business Statistics: A First Course, 8th Edition

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SOLUTIONSMANUALGAILILLICHPAULILLICHMcLennan Community CollegeSoutheast Community CollegeBUSINESSSTATISTICS:AFIRSTCOURSEEIGHTHEDITIONDavid M. LevineBaruch College, City University of New YorkKathryn A. SzabatLa Salle UniversityDavid F. StephanTwo Bridges Instructional Technology

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Table of ContentsTeaching Tips...................................................................................................................................1Chapter 1Defining and Collecting Data ...................................................................................29Chapter 2Organizing and Visualizing Variables ......................................................................37Chapter 3Numerical Descriptive Measures............................................................................145Chapter 4Basic Probability.....................................................................................................187Chapter 5Discrete Probability Distributions...........................................................................197Chapter 6The Normal Distribution.........................................................................................229Chapter 7Sampling Distributions ...........................................................................................263Chapter 8Confidence Interval Estimation ..............................................................................289Chapter 9Fundamentals of Hypothesis Testing: One-Sample Tests ......................................327Chapter 10Two-Sample Tests and One-Way ANOVA...........................................................373Chapter 11Chi-Square Tests.....................................................................................................447Chapter 12Simple Linear Regression .......................................................................................469Chapter 13Multiple Regression ................................................................................................519Chapter 14Business Analytics ..................................................................................................557Chapter 15Statistical Applications in Quality Management (Online)......................................595

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6Teaching TipsChapter 1You need to continue the discussion of the Define task by establishing the types of variables. Mention theimportance of having an operational definition for each variable. Be sure to discuss the different typescarefully since the ability to distinguish between categorical and numerical variables will be crucial laterin the course. Go over examples of each type of variable and have students provide examples of eachtype. Then, if you wish, you can cover the different measurement scales.Then move on to the C of the DCOVA approach, collecting data. Mention the different sources ofdata and make sure to cover the fact that data often needs to be cleaned of errors. Then, you could spendsome time discussing sampling, even if it is just using the table of random numbers to select a randomsample. You may want to take a bit more time and discuss the types of survey sampling methods andissues involved with survey sampling results. TheThink About Thisessay discusses the important issue ofthe use of Web-based surveys.There is also a section on Data Cleaning that discusses the issues that occur in data collection.This is followed by a section on data formatting that includes the important concepts of stacking andunstacking variables and recoding variables. The last section discusses the types of errors that occur insurveys.The chapter also introduces three continuing cases -- theManaging Ashland MultiCommServices,CardioGood Fitness, andClear Mountain State Student Surveysthat appear at the end of manychapters. The Digital cases 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 each chapter. The goal ofthe Digital cases is for students to develop skills needed to identify misuses of statistical information. Aswould be the situation with many real world cases, in Digital cases, students often need to sift throughclaims and assorted information in order to discover the data most relevant to a case task. They will thenhave to examine whether the conclusions and claims are supported by the data. (Instructional tips forusing theManaging Ashland MultiComm Services,and Digital cases and solutions to theManagingAshland MultiComm Service,CardioGood Fitness, Clear Mountain State Student Surveys, and Digitalcases are included in thisInstructor’s Solutions Manual.).Make sure that students read the Excel Guide and/or JMP Guide or Minitab Guide at the end ofeach chapter. TheIn-Depth Excelinstructions provide step-by-step instructions and live worksheets thatautomatically update when data changes. ThePHStatadd-ininstructions provide instructions for usingthe PHStat add-in.Analysis ToolPakinstructions provide instructions for using the Analysis ToolPak, theExcel add-in package that 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. If you aregoing to collect sample data to use in Chapters 2 and 3, you can illustrate sampling by conducting asurvey of students in your class. Ask each student to collect his or her own personal data concerning thetime it takes to get ready to go to class in the morning or the time it takes to get to school or home fromschool. First, ask the students to write down a definition of how they plan to measure this time. Then,collect the various answers and read them to the class. Then, a single definition could be provided (suchas the time to get ready is the time measured from when you get out of bed to when you leave your home,recorded to the nearest minute). In the next class, select a random sample of students and use the datacollected (depending on the sample size) in class when Chapters 2 and 3 are discussed. Then, move on tothe Organize step that involves setting up your data in an Excel, JMP, Minitab, or Tableau. Show thesummary worksheet and develop tables to help you prepare charts and analyze your data. Begin yourdiscussion for categorical data with the example on p. 45 concerning the percentage of the timemillennials use different devices for watching televisionand then if you wish, explain that you cansometimes organize the data into a two-way table that has one variable in the row and another in thecolumn.Continue with organizing data (but now for numerical data) by referring to the cost of a restaurantmeal on p. 49. Show the simple ordered array and how a frequency distribution, percentage distribution,or cumulative distribution can summarize the raw data in a way that is more useful.Now you are ready to tackle the Visualize step. A good way of starting this part of the chapter is todisplay 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 JMP orMinitab or Tableau to construct many different types of charts. Return to the data previously discussed onwhat devices millennials use to watch television and illustrate how a bar chart and pie chart can beconstructed. Mention their advantages and disadvantages. A good example is to show the data onincomplete ATM transactions on p. 60 and how the Pareto chart enables you to focus on the vital fewcategories. 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 simple stem-and-leaf display that both organizes the data and shows a bar type chart. Then move on to the histogramand the various polygons, pointing out the advantages and disadvantages of each.

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8Teaching TipsIf 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.If the opportunity is available, we believe that it is worth the time to cover Section 2.9 on Pitfalls inOrganizing and Visualizing Data. This is a topic that students very much enjoy since it allows for a greatdeal of classroom interaction. After discussing the fundamental principles of good graphs, try to illustratethe improper display shown in Figure 2.31. Ask students what is “bad” about this figure. Follow up with ahomework assignment involving Problems 2.69 – 2.73 (USA Todayis a great source).You will find that the chapter review problems provide large data sets with numerous variables.Report writing exercises provide the opportunity for students to integrate written and/or oral presentationwith 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 Services andclaims that have been made. The CardioGood Fitness case focuses on developing a customer profile for amarket research team. The ChoiceIsYours Follow-up expands on the chapter discussion of the mutualfunds data. The Clear Mountain State Student Survey provides data collected from a sample ofundergraduate students and a separate sample of graduate students.The Excel Guide and the JMP and Minitab and Tableau Guides for this and the remainingchapters are organized according to the sections of the chapter. They are quite extensive since they coverboth organizing and 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 youprefer.

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Teaching Tips9Chapter 3This chapter on descriptive numerical statistical measures represents the initial presentation of statisticalsymbols in the text. Students who need to review arithmetic and algebraic concepts may wish to refer toAppendix A for a quick review or to appropriate texts (seewww.pearson.com) or videos(www.videoaidedinstruction.com). Once again, as with the tables and charts constructed for numericaldata, it is useful to provide an interesting set of data for classroom discussion. If a sample of students wasselected earlier in the semester and data concerning student time to get ready or commuting time werecollected (see Chapters 1 and 2), use these data in developing the numerous descriptive summarymeasures in this chapter. (If they have not been developed, use other data for classroom illustration.)Discussion of the chapter begins with the property of central tendency. We have found 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 your classroomexample. Emphasize the effect of extreme values on the arithmetic mean and point out that the mean islike the center of a seesaw -- a balance point. Note that you will return to this concept later when youdiscuss the variance and the standard deviation. You might want to introduce summation notation at thispoint and express the arithmetic mean in formula notation as in Equation (3.1). (Alternatively, you couldwait until you cover the variance and standard deviation.) A classroom example in which summationnotation is reviewed is usually worthwhile. Remind the students again that Appendix A includes a reviewof arithmetic and algebra and summation notation [or refer them to other text sources such as those foundatwww.pearson.comor videos (seewww. videoaidedinstruction.com)].The next statistic to compute is the median. Be sure to remind the students that the median as ameasure of position must have all the values ranked in order from lowest to highest. Be sure to have thestudents compare the arithmetic mean to the median and explain that this tells us something about anotherproperty of data (skewness). Following the median, the mode can be briefly discussed. Once again, havethe students compare this result to those of the arithmetic mean and median for your data set. If timepermits, you can also discuss the geometric mean which is heavily used in finance.The completion of the discussion of central tendency leads to the second characteristic of data,variability. Mention that all measures of variation have several things in common: (1) they can never benegative, (2) they will be equal to 0 when all values are the same, (3) they will be small when there isn'tmuch variation, and (4) they will be large when there is a great deal of variation.The first measure of variability to consider is the simplest one, the range. Be sure to point out thatthe range only provides information about the extremes, not about the distribution between the extremes.Point out that the range lacks one important ingredient, the ability to take into account each datavalue. Bring up the idea of computing the differences around the mean, but then return to the fact that as

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10Teaching Tipsthe balance point of the seesaw, these differences add up to zero. At that point, ask the students what theycan do mathematically to remove the negative sign for some of the values. Most likely, they will answerby telling you to square them (although someone may realize that the absolute value could be taken).Next, you may want to define the squared differences as a sum of squares. Now you need to have thestudents realize that the number of values being considered affects the magnitude of the sum of squareddifferences. Therefore, it makes sense to divide by the number of values and compute a measure calledthe variance. If a population is involved, you divide byN, the population size, but if you are using asample, you divide byn– 1, to make the sample result a better estimate of the population variance. Youcan finish the development of variation by noting that since the variance is in squared units, you need totake the square root to compute the standard deviation.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 two datasets have vastly different standard deviations, but also vastly different means. A good example is one thatinvolves the volatility of stock prices. Point out that the variation of the price should be considered in thecontext of the magnitude of the arithmetic mean. By changing values in the data provided, students canobserve how the mean, median, and standard deviation are affected.The final measure of variation is theZscore. Point out that this provides a measure of variation instandard deviation units. You can also say that you will return toZscores in Chapter 6 when the normaldistribution will be discussed.You are now ready to move on to the third characteristic of data, shape. Be sure to clearly defineand illustrate both symmetric and skewed distributions by comparing the mean and median. You may alsowant to briefly mention the property of kurtosis which is the relative concentration of values in the centerof the distribution as compared to the tails. This statistic is provided by Excel through an Excel functionor the Analysis Toolpak and by JMP or Minitab. Once these three characteristics have been discussed,you are ready to show how they can be computed using Excel or JMP or Minitab.Now that these measures are understood, you can further explore data by computing the quartiles,the interquartile range, the five number summary, and constructing a boxplot. You begin by determiningthe quartiles. Reference here can be made to the standardized exams that most students have taken, andthe quantile scores that they have received (97th percentile, 48th percentile, 12th percentile, …, etc.).Explain that the 1stand 3rdquartiles are merely two special quantiles -- the 25th and 75th, that unlike themedian (the 2ndquartile), are not at the center of the distribution. Once the quartiles have been computed,the interquartile range can be determined. Mention that the interquartile range computes the variation inthe center of the distribution as compared to the difference in the extremes computed by the range.

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Teaching Tips11You can then discuss the five-number summary of minimum value, first quartile, median, thirdquartile, and maximum value. Then, you construct the boxplot. Present this plot from the perspective ofserving as a tool for determining the location, variability, and symmetry of a distribution by visualinspection, and as a graphical tool for comparing the distribution of several groups. It is useful to displayFigure 3.9 on page 142 that indicates the shape of the boxplot for four different distributions. Then, usePHStat or JMP or Minitab or Tableau to construct a boxplot. Note that you can construct the boxplot for asingle group or for multiple groups.If you desire, you can discuss descriptive measures for a population and introduce the empiricalrule 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 between twonumerical variables. Point out that the coefficient of correlation has the advantage as compared to thecovariance of being on a scale that goes from –1 to +1. Figure 3.11 on p. 157 is useful in depicting scatterplots for different coefficients of correlation.Once again, you will find that the chapter review problems provide large data sets with numerousvariables.TheManaging Ashland MultiComm Servicescase enables students to examine the use ofdescriptive statistics in an actual business environment. The Digital case continues the evaluation of theEndRun Financial Services discussed in the Digital case in Chapter 2. The CardioGood Fitness casefocuses on developing a customer profile for a market research team. More Descriptive Choices Follow-up expands on the discussion of the mutual funds data. The Clear Mountain State Student Surveyprovides data collected from a sample of undergraduate students and a separate sample of graduatestudents.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 a list ofstatistics. PHStat can be used to construct a boxplot. Or you can use JMP or Minitab. The Tableau guidecovers the five number summary and the boxplot

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12Teaching TipsChapter 4The chapter on probability represents a bridge between the descriptive statistics already covered and thetopics of statistical inference and regression to be covered in subsequent chapters. In many traditionalstatistics courses, often a great deal of time is spent on probability topics that are of little directapplicability in basic statistics. The approach in this text is to cover only those topics that are of directapplicability in the remainder of the text.You need to begin with a relatively concise discussion of some probability rules. Essentially,students really just need to know that (1) no probability can be negative, (2) no probability can be morethan 1, and (3) the sum of the probabilities of a set of mutually exclusive events adds to 1.0. Studentsoften understand the subject best if it is taught intuitively with a minimum of formulas, with an examplethat relates to a business application shown as a two-way contingency table (see the Using Statisticsexample). If desired, you can use In-Depth Excel or PHStat to compute probabilities from thecontingency 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. Inaddition, 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 be ofmarginal importance. The Digital case in this chapter extends the evaluation of the EndRun FinancialServices to consider claims made about various probabilities. The CardioGood Fitness, More DescriptiveChoices Follow-up, and Clear Mountain State Student Survey each involve developing contingency tablesto be able to compute and interpret conditional and marginal probabilities.

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Teaching Tips13Chapter 5Now that the basic principles of probability have been discussed, the probability distribution is developedand the expected value and variance (and standard deviation) are computed and interpreted. Given that aprobability distribution has been defined, you can now discuss some specific distributions. Althoughevery introductory course undoubtedly covers the normal distribution to be discussed in Chapter 6, thedecision about whether to cover the binomial or Poisson distributions is a matter of personal choice anddepends on whether the course is part of a two-course sequence.If the binomial distribution is covered, an interesting way of developing the binomial formula isto 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 a sampleof 4. Usually a response will be elicited that provides three items of interest out of four selections in aparticular order such as Tagged Tagged Not Tagged Tagged. Ask the class, what would be the probabilityof getting Tagged on the first selection? When someone responds 0.1, ask them how they found thatanswer and what would be the probability of getting Tagged on the second selection. When they answer0.1 again, you will be able to make the point that in saying 0.1 again, they are assuming that theprobability of Tagged stays constant from trial to trial. When you get to the third selection and thestudents respond 0.9, point out that this is a second assumption of the binomial distribution -- that onlytwo outcomes are possible -- in this case Tagged and Not Tagged, and the sum of the probabilities ofTagged and Not Tagged must add to 1.0. Now you can compute the probability of three out of four inthis order by multiplying (0.1)(0.1)(0.9)(0.1) to get 0.0036. Ask the class if this is the answer to theoriginal question. Point out that this is just one way of getting three Tagged out of four selections in aspecific order, and, that there are four ways to get three Tagged out of four selections This leads to thedevelopment of the binomial formula Equation (5.4). You might want to do another example at this pointthat calls for adding several probabilities such as three or more Tagged, less than three Tagged, etc.Complete the discussion of the binomial distribution with the computation of the mean and standarddeviation of the distribution. Be sure to point out that for samples greater than five, computations canbecome unwieldy and the student should use PHStat, an Excel function, the binomial tables (See theOnlineBinomial.pdftables), JMP, or Minitab.Once the binomial distribution has been covered, if time permits, other discrete probabilitydistributions can be presented. If you cover the Poisson distribution, point out the distinction between thebinomial and Poisson distributions. Note that the Poisson is based on an area of opportunity in which youare counting occurrences within an area such as time or space. Contrast this with the binomial distributionin which each value is classified as of interest or not of interest. Point out the equations for the mean and

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14Teaching Tipsstandard deviation of the Poisson distribution and indicate that the mean is equal to the variance. Since thecomputation of probabilities from these discrete probability distributions can become tedious for otherthan small sample sizes, it is important to discuss PHStat, an Excel function the Poisson tables (See theOnlinePoisson.pdftables) or JMP or Minitab.TheManaging Ashland MultiComm Servicescase for this chapter relates to the binomialdistribution. The Digital case involves the expected value and standard deviation of a probabilitydistribution and applications of the covariance in finance.

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Teaching Tips15Chapter 6Now that probability and probability distributions have been discussed in Chapters 4 and 5, you are readyto introduce the normal distribution. We recommend that you begin by mentioning some reasons that thenormal distribution is so important and discuss several of its properties. We would also recommend thatyou do not show Equation (6.1) in class as it will just intimidate some students. You might begin byfocusing on the fact that any normal distribution is defined by its mean and standard deviation and displayFigure 6.3 on p. 234. Then, an example can be introduced and you can explain that if you subtracted themean from a particular value, and divided by the standard deviation, the difference between the value andthe mean would be expressed as a standardized normal orZscore that was discussed in Chapter 3. Next,use Table E.2, the cumulative normal distribution, to find probabilities under the normal curve. In thetext, the cumulative normal distribution is used since this table is consistent with results provided byExcel, JMP, and Minitab. Make sure that all the students can find the appropriate area under the normalcurve in their 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 word area issynonymous with the word probability. Once this has been accomplished, a good approach is to workthrough a series of examples with the class, having a different student explain how to find each answer.The example that will undoubtedly cause the most difficulty will be finding the values corresponding toknown probabilities. Slowly go over the fact that in this type of example, the probability is known and theZvalue needs to be determined, which is the opposite of what the student has done in previous examples.Also point out that in cases in which the unknownXvalue is below the mean, the negative sign must beassigned to theZvalue. Once the normal distribution has been covered, you can use PHStat, or variousExcel functions or JMP or Minitab to compute normal probabilities. You can also use the VisualExplorations in Statistics Normal distribution procedure on p. 239. This will be useful if you intend touse examples that explore the effect on the probabilities obtained by changing theXvalue, the populationmean,, or the standard deviation,.TheThink About Thisessay provides a historical perspective ofthe application of the normal distribution.If you have sufficient time in the course, the normal probability plot can be discussed. Be sure tonote that all the data values need to be ranked in order from lowest to highest and that each value needs tobe converted to a normal score. Again, you can either use PHStat to generate a normal probability plot,use Excel functions with Excel charts, or use JMP or Minitab.TheManaging Ashland MultiComm Servicescase for this chapter relates to the normaldistribution. The Digital case involves the normal distribution and the normal probability plot. TheCardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain State Student Surveyeach involve developing normal probability plots.

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16Teaching TipsChapter 7The coverage of the normal distribution in Chapter 6 flows into a discussion of sampling distributions.Point out the fact that the concept of the sampling distribution of a statistic is important for statisticalinference. Make sure that students realize that problems in this section will find probabilities concerningthe mean, not concerning individual values. It is helpful to display Figure 7.4 on p. 265 to show how theCentral Limit Theorem applies to different shaped populations. A useful classroom or homework exerciseinvolves using PHStat, Excel, or JMP or Minitab to form sampling distributions. This reinforces theconcept of the Central Limit Theorem.TheManaging Ashland MultiComm Servicescase for this chapter relates to the samplingdistribution of the mean. The Digital case also involves the sampling distribution of the mean.You might want to have students experiment with using the Visual Explorations add-in workbookto explore sampling distributions. You can also use either Excel functions, the PHStat add-in, theAnalysis ToolPak, or JMP or Minitab to develop sampling distribution simulations.

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Teaching Tips17Chapter 8You should begin this chapter by reviewing the concept of the sampling distribution covered in Chapter 7.It is important that the students realize that (1) an interval estimate provides a range of values for theestimate of the population parameter, (2) you can never be sure that the interval developed does includethe population parameter, and (3) the proportion of intervals that include the population parameter withinthe interval is equal to the confidence level.Note that the Using Statistics example for this chapter, which refers to the Ricknel Home Centersis actually a case study that relates to every part of the chapter. This scenario is a good candidate for useas the classroom example demonstrating an application of statistics in accounting. It also enables you touse the DCOVA approach of Define, Collect, Organize, Visualize, and Analyze in the context ofstatistical inference.When introducing thetdistribution for the confidence interval estimate of the population mean,be sure to point out the differences between thetand normal distributions, the assumption of normality,and the robustness of the procedure. It is useful to display Table E.3 in class to illustrate how to find thecriticaltvalue. When developing the confidence interval for the proportion, remind the students that thenormal distribution may be used here as an approximation to the binomial distribution as long as theassumption of normality is valid [whennand(1)nare at least 5].Having covered confidence intervals, you can move on to sample size determination by turningthe initial question of estimation around, and focusing on the sample size needed for a desired confidencelevel and width of the interval. In discussing sample size determination for the mean, be sure to focus onthe need for an estimate of the standard deviation. When discussing sample size determination for theproportion, be sure to focus on the need for an estimate of the population proportion and the fact that avalue of0.5 can be used in the absence of any other estimate.Since the formulas for the confidence interval estimates and sample sizes discussed in this chapterare straightforward, using PHStat or In-Depth Excel can remove much of the tedious nature of thesecomputations or you can use JMP or Minitab.TheManaging Ashland MultiComm Servicescase for this chapter involves developing variousconfidence intervals and interpreting the results in a marketing context. The Digital case also relates toconfidence interval estimation. This chapter marks the first appearance of the Sure Value ConvenienceStore case which places the student in the role of someone working in the corporate office of a nationwidec0nvenience store franchise. This case will appear in the next two chapters, Chapters 9 – 10. TheCardioGood Fitness, More Descriptive Choices Follow-up, and Clear Mountain State Student Surveyeach involve developing confidence interval estimates.

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