Solution Manual for Business Statistics, 4th Edition

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INSTRUCTOR'SSOLUTIONSMANUALFORBUSINESSSTATISTICSLINDADAWSONUniversity of WashingtonBUSINESSSTATISTICS4THEDITIONNOREANR.SHARPESt. John’s UniversityRICHARDD.DEVEAUXWilliams CollegePAULF.VELLEMANCornell University

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Table of ContentsPart IExploring and Collecting DataChapter 1Dataand Decisions1-1Chapter 2Displaying and Describing Categorical Data2-1Chapter 3Displaying and Describing Quantitative Data3-1Chapter 4Correlation and LinearRegression4-1Case Study: Paralyzed Veterans of America4-49Part IIModeling with ProbabilityChapter 5Randomness and Probability5-1Chapter 6Random Variables and Probability Models6-1Chapter 7The Normal and Other Continuous Distributions7-1Part IIIGathering DataChapter 8Data Sources: Observational Studies and Surveys8-1Chapter 9Data Sources:Experiments9-1Part IVInference for Decision MakingChapter 10Sampling Distributions and ConfidenceIntervals for Proportions10-1Case Study: Real Estate SimulationChapter 11Confidence Intervals for Means11-1Chapter 12Testing Hypotheses12-1Chapter 13More about Tests and Intervals13-1Chapter 14Comparing Two Means14-1Chapter 15Inference forCounts: Chi-Square tests15-1Brief Case:Loyalty Program15-27Part VModels for Decision MakingChapter 16Inference for Regression16-1Chapter 17Understanding Residuals17-1Chapter 18MultipleRegression18-1

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Chapter 19Buidling Multiple Regression Models19-1Chapter 20Time Series Analysis20-1Case Study:Health Care Costs20-33Part VIAnalyticsChapter 21Introduction to Big Data and Data Mining21-1Part VIIOnline TopicsChapter 22Quality Control22-1Chapter 23Nonparametric Methods23-1Chapter 24Decision Making and Risk24-1Chapter 25Analysis of Experiments and Observational Studies25-1

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1-1Chapter1–Dataand DecisionsSECTION EXERCISESSECTION1.11.a)Each row represents a different housethat was recently sold.Itcan bedescribed as a case.b)There aresixquantitativevariables in each rowplus a house identifierfor a total of seven variables.2.a)Each row represents a different transaction (not customer or book). Itcan bedescribed asa case.b)There aresix quantitativevariablesplus two identifiersin each rowfor a total of eight variables.SECTION1.23.a)House_ID is an identifier (categorical, not ordinal); Neighborhood is categorical(nominal); Mail_ZIP iscategorical (nominal–ordinal in a sense, but only on a national level);Acresis quantitative (units–acres);Yr_Builtis quantitative (units–year); Full_Market_Valueis quantitative (units–dollars); Sizeisquantitative (units–squarefeet).b)These data are cross-sectional. Each row corresponds to a housethat recentlysoldso at approximatelythe samefixedpoint intime.4.a)Transaction ID is an identifier (categorical, nominal, not ordinal); Customer ID is an identifier(categorical, nominal);Datecan be treated asquantitative(how many dayssince the transaction took place,days since Jan. 1 2009, for example)orcategorical (as month, for example); ISBN isan identifier(categorical, nominal); Price is quantitative (units–dollars); Coupon is categorical(nominal); Gift iscategorical (nominal); Quantity is quantitative (unit–counts).b)These data are cross-sectional. Each row corresponds to a transaction at a fixedpoint intime. However,the date of the transaction has been recordedsothe datacouldbe reconfigured as a time series.It is likelythat the store had more sales in that time period so a time series is not appropriate.SECTION1.35.It is not specified whether or not thereal estate data of Exercise 1 areobtained froma survey. The datawould not be from anexperiment, a data gathering method with specific requirements. Rather, the realestate major’s data set was derived from transactional data (on local home sales). The major concern withdrawing conclusions from this data set is that we cannot be sure that the sample is representative of thepopulationof interest(e.g.,all recent local home salesor even all recent national home sales).Therefore,we should be cautious about drawing conclusions from these data about the housing market in general.6.The student is using a secondary data source (from the Internet).No informationis given about how, when,where and why these data were collectedor if it was the result of a designed experiment.It isalsonotstated thatthesampleis representativeof companies.There areconcerns about using these data forgeneralizing anddrawing conclusionsbecausethe datacould have beencollected for a different purpose(not necessarily for developing a stock investment strategy).Therefore, the student should becautiousabout using this type of data to predict performance in the future.CHAPTER EXERCISES7.The news.Answers will vary.8.The Internet.Answers will vary.9.Survey.The description of the study has to be broken down into its components in order to understand thestudy.Who–who or what was actually sampled–college students;What–what is being measured–opinion ofelectric vehicles: whether there will more electric or gasoline powered vehicles in 2025 and thelikelihoodof whether they wouldpurchase an electric vehiclein the next 10 years;When–current;Where–yourlocation;Why–automobilemanufacturer wants college student opinions;How–how was the study

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1-2Chapter1Dataand Decisionsconducted–survey;Variables–thereare twocategoricalvariables–what students think about whether or notthere will be more electric or gasoline powered vehicles in 2025 andthe secondcategorical variable isalsoordinal–how likely, using a scale,would the student be to buy an electric vehicle in the next 10 years;Source–thedataare not from a designed survey or experiment;Type–thedata arecross-sectional;Concerns–none.10.Yoursurvey.Answers will vary.11.World databank.Answers will vary but chosen from the following possible indicators:•GDP growth (annual %)•GDP (current US$)•GDP per capita (current US$)•GNI per capita, Atlas method (current US$)•Exports of goods and services (% of GDP)•Foreign direct investment, net inflows (BoP, current US$)•GNI per capita, PPP (current international $)•GINI index•Inflation, consumer prices (annual %)•Population, total•Life expectancy at birth, total (years)•Internet users (per 100 people)•Imports of goods and services (% of GDP)•Unemployment, total (% of total labor force)•Agriculture, value added (% of GDP)•CO2 emissions (metric tons per capita)•Literacy rate, adult total (% of people ages 15 and above)•Central government debt, total (% of GDP)•Inflation, GDP deflator (annual %)•Poverty headcount ratio at national poverty line (% of population)12.Arby’s menu.Who–Arby’s sandwiches;What–type of meat, number of calories (in calories), and servingsize (in ounces);When–not specified;Where–Arby’s restaurants;Why–assess the nutritional value of thedifferent sandwiches;How–information was gathered from each of the sandwiches on the menu at Arby’s,resulting in a census;Variables–there are 3 variables:the number of calories and serving size arequantitative, and the type of meat is categorical;Source–dataare not from a designed survey or experiment;Type–data are cross-sectional;Concerns–none.13.MBA admissions.Who–MBA applicants(innortheastern U.S.);What–sex, age, whether or not accepted,whether or not they attended, and the reasons for not attending (if they did not accept);When–not specified;Where–a school in the northeastern United States;Why–the researchers wanted to investigate any patternsin female student acceptance and attendance in the MBA program;How–data obtained from the admissionsoffice;Variables–there are 5 variables:sex, whether or not the students accepted, whether or not theyattended, and the reasons for not attending if they didnot accept (all categorical) and age which isquantitative;Source–data are not from a designed survey or experiment;Type–data are cross-sectional;Concerns–none.14.MBAadmissions II.Who–MBA students(inprogram outside of Paris);What–each student’s standardizedtest scores and GPA in the MBA program;When–2009to2014;Where–outside of Paris;Why–toinvestigate the association between standardized test scores and performance in the MBA program overfive years (2009–2014);How–not specified;Variables–there are 2 quantitative variables:standardized testscores and GPA;Source–data are not from a designed survey or experiment, data are available from studentrecords;Type–although the data are collected over 5 years, the purpose is toexamine them as cross-sectional rather than astime-series;Concerns–none.

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Chapter1Data and Decisions1-315.Pharmaceutical firm.Who–experimentalvolunteers;What–herbal cold remedy or sugar solution, and coldseverity;When–not specified;Where–major pharmaceutical firm;Why–scientists were testing theeffectiveness of an herbal compound on the severity of the common cold;How–scientists conducted acontrolled experiment;Variables–there are 2 variables:type of treatment (herbal or sugar solution) iscategorical, and severity rating is quantitative;Source–datacomefrom an experiment;Type–data arecross-sectionaland from a designed experiment;Concerns–the severity of a cold might be difficult toquantify (beneficial to add actual observations and measurements, such as bodytemperature). Also,scientists at a pharmaceutical firm could have a predisposed opinion about the herbal solution or may feelpressure to report negative findings about the herbal product.16.Start-up company.Who–customers of a start-up company;What–customer name, ID number, region ofthecountry(coded as1 = East, 2 = South, 3 = Midwest, 4 = West), date of last purchase, amount ofpurchase ($), and item purchased;When–present day;Where–not specified;Why–the company is building adatabase ofcustomers and sales information;How–assumed that the company records the neededinformation from each new customer;Variables–there are 6 variables: name, ID number, region of thecountry, and item purchased which are categorical anddate and amount of purchaseare quantitative. Datecould be coded as categorical as well;Source–data are not from a designed survey or experiment;Type–data are cross-sectional;Concerns–although region is coded as a number, it is still a categorical variable.17.Vineyards.Who–vineyards;What–sizeof vineyard(most likely inacres), number of years in existence,state, varieties of grapes grown, average case price ($), gross sales ($), and percent profit;When–notspecified;Where–not specified;Why–business analysts hope to provide information that would be helpfultoproducers ofU.S. wines;How–questionnaireto a sample of growers;Variables–there are 5 quantitativevariables: thesize of vineyard (acres), number of years in existence, average case price ($), gross sales ($);there are 2 categorical variables: state and variety of grapes grown;Source–data come from a designedsurvey;Type–data are cross-sectional;Concerns–none.18.Spectrem group polls.Who–not completely clear. Probably asample of affluent and retired people;What–pet preference, number of pets, services and products bought for pets (from a list);When–not specified;Where–United States;Why–provide servicesfortheaffluent;How–survey;Variables–there are 3categorical variables:pet preference, list of pets and list of services and products bought for pet;Source–data from a designed survey;Type–data are cross-sectional;Concerns–none.19.EPA.Who–every model of automobile in the United States;What–vehicle manufacturer, vehicle type (car,SUV, etc.), weight (probably pounds), horsepower (units of horsepower), and gas mileage (miles pergallon) for city and highway driving;When–the information is currently collected;Where–United States;Why–the EPA uses the information to track fuel economy of vehicles;How–among the data EPA analystscollect from the automobile manufacturers are the name of the manufacturer (Ford, Toyota, etc.), vehicletype….”;Variables–there are 6 variables:vehicle manufacturer and vehicle typeare categorical variables;weight, horsepower, andgas mileagefor both city and highway driving are quantitative variables;Source–data are not from a designed survey or experiment;Type–data are cross-sectional;Concerns–none.20.Consumer Reports.Who–46 models of smart phones;What–brand, price (probably dollars), display size(probably inches) operating system, camera image size (megapixels), and memory card slot (yes/no);When–not specified;Where–not specified;Why–the information was compiled to provide information toreaders of Consumer Reports;How–not specified;Variables––there area total of 6 variables:price,display size andimage sizeare quantitative variables;brandandoperating systemare categorical variables,and memory card slotis a nominal variable;Source–not specified;Type–thedata are cross-sectional;Concerns–this many or may not be a representative sample ofsmart phones, or includes all of them, wedon’t know.This is a rapidly changing market, so their data are at best a snapshot of the state of the marketat this time.21.Zagat.Who–restaurants;What–% of customers liking restaurant, average meal cost ($), food rating (0-30),decor rating (0-30), service rating (0-30);When–current;Where–not specified;Why–service to provideinformation for consumers;How–not specified;Variables–there are 5 variables:% liking and average cost

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1-4Chapter1Dataand Decisionsare quantitativevariables;ratings (food, decor and service) are ordered categories, therefore, ordinalvariables;Source–not specified;Type–thedata are cross-sectional.22.L.L. Bean.Who–catalogmailings;What–number of catalogs mailed out, square inches in catalog, and sales($ million) in 4 weeks following mailing;When–current;Where–L.L. Bean (United States);Why–toinvestigate association among catalog characteristics, timing, and sales;How–collection ofinternal data;Variables–there are 3 variables: number of catalogs, square inches incatalog, and salesare all quantitativevariables;Source–not specified;Type–data are cross-sectional;Concerns–none.23.Stockmarket.Who–students in an MBA statistics class;What–total personal investment in stock market($), number of different stocks held, total invested in mutual funds ($), and the name of each mutual fund;When–not specified;Where–a business school in the northeast US;Why–the information was collected foruse in classroom illustrations;How–an online survey was conducted, participation was probably requiredfor all members of the class;Variables–there are 4 variables: total personal investment instock market,number of different stocks held, total invested in mutual fundsare quantitative variables; the name of eachmutual fund is a categorical variable;Source–data come from a designed survey;Type–data are cross-sectional.24.Theme park sites.Who–potential theme park locationsin Europe;What–country of site, estimated cost(probably€), potential population size (counts), size of site (probablyhectares), whether or not masstransportation within 5 minutes of site;When–2013;Where–Europe;Why–to present to potential developerson the feasibility of various sites;How–not specified;Variables–there are 5 variables: country of site andwhether or not mass transportationiswithin 5 minutes of site are both categorical variables;estimated cost,potential population size and size of site are quantitativevariables;Source–data are not from a designedsurvey or experiment;Type–data are cross-sectional.25.Taxi data.Who–taxi rides in NYC;What–vendor ID,pickup time,dropoff time,number passengers, tripdistance, pickup longitude and latitude, dropoff longitude and latitude, fare amount, tip amount, tollamount, total amount;Where–New York City;Why–market analysis of taxi rides;How–the New York CityTaxi and Limousine Commission records the trip information;Variables––there are13variables:numberof passengers, trip distance, pickup and dropoff longitude and latitude, fare amount, tip amount, tollamount, total amount, and the date and time of pickup are quantitative(dates could also be consideredcategorical);Source–NYC Taxi and Limousine Commission;Type–data arecross-sectional;Concerns–none.26.Dalia Research.Who–43,034people worldwide who responded to the Dalia survey;What–ID #, age, planto purchase car,city/rural, mobile device, education, gender, latitude, longitude, country, town size,household size;When–not specified in problem;Where–worldwide;Why–Dalia collects data about a widevariety of topics for market research purposes;How–survey sent to an unspecified number of peopleworldwide;Variables–there are12variablesin the subset of data presented:age, latitude and longitude arequantitative. Plan to purchase car, city or rural, mobile device, education, gender, country, and town sizeare categorical. ID is an identifier.Town size, household size, and education are also ordinal;Source–surveyresults;Type–data arecross-sectional;Concerns–none.27.Mortgages.Each row represents each individual mortgage loan. Headings of the columns would be:loannumber (the row identifier), last 4 numbers of the borrower’s social security number,mortgage amount,borrower’s name.28.Employee performance.Each row represents each individual employee. Headings of the columns wouldbe: Employee ID Number (to identify the row instead of name), contract average ($), supervisor’s rating (1-10), and years with the company.29.Company performance.Each row represents a week. Headings of the columns would be: week number ofthe year (to identify each row), sales prediction ($), sales ($), and difference between predicted sales andrealized sales ($).

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Chapter1Data and Decisions1-530.Command performance.Each row represents a Broadway show. Headings of the columns would be: theshow name (identifies the row), profit or loss ($), number ofinvestorsand investment total ($).31.Car sales.Cross-sectional are datataken from situations that vary over time but measured at a singletimeinstant.This problem focuses on data for September only which is a single time period.Therefore, the data are cross-sectional.32.Motorcycle sales.Time-series data are measured over time.Usually the time intervals are equally-spaced (e.g. every week, every quarter, or every year). This problem focuses on the number ofmotorcycles sold by the dealership in each month of 2014; therefore, the data are measuredover aperiod of time and are time series data.33.Forestry.Time-series data are measured over time.Usually the time intervals are equally-spaced (e.g.every week, every quarter, or every year). This problem focuses on the average diameter of treesbrought to a sawmill in each week of a year; therefore, the data are measuredover a period of timeand are time-series data.34.Baseball.Cross-sectional are datataken from situations that vary over time but measured at a singletime instant.This problem focuses on data for attendance of the third World Series game. Therefore,the data are cross-sectional.

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1-6Chapter1Dataand DecisionsEthics in ActionSarah’s dilemma:The company RSPT Inc.is having Sarah compare their strategies to other companies. However,they could influence the outcome by funding the research and providing free software. In addition, Sarah may feelobliged to favor RSPT Inc. because they were generous in providing her research tools and funding. The companymay put pressure on her to favor their methods over others because of their close relationship. The undesirableconsequences are that the results are not completely objective and bias exists due to the funding circumstances.One possible solution would be to find other grants outside of RSPT Inc. but not connected to any of the companiesbeing compared. This might also be true of the software. It is important in a scientific study to be completelyobjective and notbe influencedby one of the clients being examined.Jim’s dilemma:Statistics and data can often be manipulated to produce a desired result that can “fudge” resultsandpresent a more desirable outcome. The scientific method is constructed to be objective if the rules are followed. Theobjective of Jim’s study was to increase the percentage of clients who viewed their advisory services as outstanding,not increase the overall satisfaction average. In presentingan increased average, Jim is not being honest about thespecific results of his study with respect to his objective.He should be honest about the decrease in the“outstanding” category.One possible solution might be to compare the number of responses in each survey to see if there is a discrepancythat could explain the change. In addition, he could point out the large increase in the “above average” category(10% to 40%) which shows a huge improvement. Many people may be unwilling to give the highest rating on anintermediate basis but would be willing to identify an improvement.For further information on the official American Statistical Association’s Ethical Guidelines, visit:http://www.amstat.org/about/ethicalguidelines.cfmTheEthical Guidelinesaddress important ethical considerations regarding professionalism and responsibilities.Brief Case–Credit Card BankList the W’s for these data:Who–bankcardholdersWhat–monthlycredit card charges made by cardholderfromAugust 2016 through April 2017,marketing segment,industry segment, amount of spend lift after promotion, average spending on card pre-and post-promotion, whetheror not cardholder is a retailor travelcustomer, and the type of spending habits.Why–to determinecustomer spending habits andwhat types of offers arebeing taken advantage of and in whatway.When–most likely in 2017Where–although not specified, most likely national datacollected in U.S.How–demographic data most likely collected when credit card account was opened and spending data collectedduring transactionsClassify each variable as categorical or quantitative; if quantitative identify the units:OfferType–categoricalEnrollment Required–categoricalCharges August 2016–quantitative ($)Charges September 2016–quantitative ($)Charges October 2016–quantitative($)ChargesNovember2016–quantitative ($)ChargesDecember2016–quantitative ($)ChargesJanuary2017–quantitative($)ChargesFebruary2017–quantitative ($)

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Chapter1Data and Decisions1-7ChargesMarch2017–quantitative ($)ChargesApril2017–quantitative($)OpportunitySegment–categoricalIndustry Segment–categoricalCombined Segment–categoricalSpend Lift–quantitative ($)

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2-1Chapter2–Displaying and Describing Categorical DataSECTION EXERCISESSECTION2.11.a)Frequency table:b)Relative frequency table (divide eachnumber by 512 and multiply by 100):2.a)Frequency table:b)Relative frequency table:SECTION2.23.a)b)NoneAABAMAPhD164422255229NoneAABAMAPhD32.03%8.20%43.95%10.16%5.66%Under 66 to 910 to 1415 to 21Over 21458315418170Under 66 to 910 to 1415 to 21Over 219.57%17.66%32.77%3.83%36.17%

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2-2Chapter2Visualizing and Describing Categorical Datac)4.a)b)c)

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Chapter2Visualizing and Describing Categorical Data2-35.a)Most employees have either a bachelor’s degree (44%) or no college degree (32%). About10%have master’s degrees, 8% have associate’s degrees, and nearly 6% have PhDs.b)It is difficult to generalize these results to any other division of the company or to any othercompany.These data were collected fromonlyonedivision. Otherdivisions andcompaniesmight have vastly different educationalrequirements for their employees and thereforedistributions of educational levels.6.a)Approximately13of the viewerswere 10–14 yearsold. Over a third (36%) of the viewers wereover the age of 21, many of whom could be parents accompanying their children.Slightly over50% of the viewers were children and younger teenagers from 6 to 14 years of age. About 10% ofthe viewers were younger children under 6 years of age. Only 4% were older teenagers to youngadults from 15 to 21 years of age.b)We do not know whether these audiences are representative.No information is givenabout howthe locations were selected, what time of daythe interviews were conducted, etc.Moreover, wedon’t knowhow many individuals did not agree to beinterviewed.Are teenagers and youngadults from 15 to 21 years of age underrepresented in the sample becausethe film was notappealing to this age group or becausethey declined to be interviewed?SECTION2.37.a)b)Yes.8.a)b)Yes.Totals< 1 year951-5 years205more than 5 years212NoneAABAMAPhD164422255229TotalsNever350Once78More than Once42Under 66 to 910 to 1415 to 21Over 21458315418170

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2-4Chapter2Visualizing and Describing Categorical DataSECTION 2.49.a)b)No. The distributions look quite different. More than 2/3 of those with no college degree havebeen with the company longer than 5years, but almost none of the PhDs (less than 7%) havebeen there that long.It appears thatwithin the last few yearsthe companyhas hired bettereducated employees.c)d)Itis easier to see the differences in the distributions in the stacked bar chart.e)A mosaic plot woulddisplay the different counts for each degree type.Areas of the plotrepresenting each cell would then reflect the cell counts accurately.10.a)b)The vast majority of viewers hadn’t seen the movie before except for the 10-to 14-year-old group,where nearly half(45.5%) had seen the movie at least once.(%)NoneAABAMAPhD< 1 year6.17.122.238.541.41-5 years25.621.449.851.951.7more than 5 years68.371.428.09.66.9(%)Under 66to 910 to 1415 to 21Over 21Never86.772.354.588.988.8Once6.724.124.711.18.8More than once6.73.620.802.4

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Chapter2Visualizing and Describing Categorical Data2-5c)d)It is easier to see the differences in the distribution in the stacked bar chart. The stacked bar chartmakes the 10to14yearoldagegroup (and to a lesserextent the 6to 9yearoldagegroup) standout as havinga larger percentage of viewers who have seen the movie at least oncebeforecompared to the other age groups.e)A mosaic plot would display the different counts in each age group accurately as well, providing abetter representation of the counts in the table.CHAPTER EXERCISES11.Graphs in the news.Answers will vary.12.Graphs in the news, part 2.Answers will vary.13.Tables in the news.Answers will vary.14.Tables in the news, part 2.Answers will vary.15.U.S.market share.a)Yes, this is an appropriate display for these data because all categories of one variable (sellers ofcarbonated drinks) are displayed. The categories divide the whole and the category Othercombines the smaller shares.b)The company with the largest share is Coca-Cola.16.Brandvalue.a)Yes, this is an appropriate display for these data.Thevariablewhich is categorical(distributors ofcarbonated beverages) are displayedand dollar value easily readable.b)The company with thesmallestshare isDr. Pepper.c)Red Bull slightly edges out Pepsi.

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2-6Chapter2Visualizing and Describing Categorical Data17.Market share again.a)The pie chart does a better job of comparing portions of the whole.b)The “Other” category is missing and without it, the results could be misleading.18.Brand valueagain.a)The barchart does a better job. The close categories are hard to compare directlyinapie chartbecause they arealmost the same sizepie segments.b)Too close to tell from the pie chart. Much easier to see from the bar chart.19.Insurance company.a)Yes, it is reasonable to conclude that deaths due to heart OR respiratory diseases is equal to 30.3%plus 7.9%, which equals 38.2%. The percentages can be added because the categories do notoverlap. There can only be oneprimarycause of death.b)The percentages listed in the table only add up to 73.7%. Therefore, other causes must account for26.3% of U.S. deaths.c)An appropriate display could either be a bar graph or a pie graph, using an “Other” category forthe remaining 26.3% causes of death.20.Financial satisfactiona)Answers may vary.Side-by-side bar charts,stacked bar charts,or mosaic plots would all be goodvisualizations.A comparison of percentages by level of satisfaction is shown in the followingsegmented bar chart. It is appropriate to compare percentages rather than individual numbers.Based on the given data,the comparison betweenfemalesandmalesshow thatboth gendershavevery comparable percentages for levels of satisfaction. It would not be reasonable to conclude thatfemales are less satisfied than males with their financial situation.b)It would not be reasonable to conclude that there are more than 50% males in the United Statesfrom the data provided because the data represent a sample, not the whole.

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Chapter2Visualizing and Describing Categorical Data2-721.B2B.Cisco and Polycom areclose to each other, battlingfor first place in theNetherlands, and theremainder of the market is fragmented.A pie chart or bar chart would be appropriate.0.310.300.380.360.160.170.130.140.030.02M A L EF E M A L EVery satisfiedSomewhat satisfiedSomewhat dissatisfiedVery dissatisfiedNo AnswerPolycom31%Cisco33%Lifesize11%SiemensOthers22%

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2-8Chapter2Visualizing and Describing Categorical Data22.Toy makers.a)Answers may vary. Sales of toysgrew nearly 15.9% from 2013 to 2016.Theonlycategorythat did notshow growthwasArts & Crafts.Outdoor& Sports Toys and Infant/Toddler/Preschool Toys were the largesttwo categories across the years, followed by Dolls closely behind in third place. In terms of percentages,between 2013 and 2016, Outdoor & Sports Toys (23%increase), Games/Puzzles (43% increase), and Dolls(25% increase) grew the most.b)Answers may vary.Plotted as raw values ($) or as a stacked bar graph, it is difficult to seethedifferences.Computing the percent of total by year and using that value in a bar graph comparing percent by years,reveals changes from 2013 to 2016for each category. Specifically, Outdoor & Sports Toys,Infant/Toddler/Preschool Toys,andDollshave the highest percentages for 2016.23.Job satisfaction.a)The percentagesdon’t total100%.Others eitherrefused to answer or didn’t know.b)Bar chart:0%2%4%6%8%10%12%14%16%18%20%Percent of Toy Sales2013 (%)2016 (%)

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Chapter2Visualizing and Describing Categorical Data2-9c)A pie chart would not be appropriatewith the data as isbecause the percentages do not represent partsof a whole and do not total 100%. A pie chart would work if“Other” category is added.24.Smallbusiness hiring.a)Thepercentages total 98%. Theother 2% either didn’t answer or didn’t know.b)Bar chart:c)A pie chart would not be appropriate because the percentages do not represent parts of a whole and donot total 100%.An “Other” category would have to be added.d)(Answers will vary)Half (50%) of the respondents said that their cash flow was very orsomewhat good (37% said somewhat). Only 27% said somewhat or very poor.25.Environmental hazard2016.The bar chart shows thatGroundingand Collisions arethe most frequent causesof oil spillage for these 460spills andallows the reader to rank the other types as well. If being able todifferentiate between close counts is required, use the bar chart. The pie chart is also acceptable as a displayandmakes it easier to see that Grounding and Collisions make up around 60% of the total causes of spillage but it is0%10%20%30%40%50%Very satisfiedSomewhatsatisfiedSomewhatdissatisfiedVerydissatisfiedOther

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2-10Chapter2Visualizing and Describing Categorical Dataharder to determine the causes that are close to each other, such as Grounding and Collisions or Hull Failure vs.Fire/Explosion.To showcase the causes of oil spills as a fraction of all 460spills, use the pie chart.26.Olympicmedals.a)If we treat the number of medals as the category, there are too many categories--most of themempty.b)Onealternative is to show only the bars for medal counts that have occurred. The risk here is that areader might not notice the missing counts.01020304050607080010203040608090250# OF COUNTRIESMEDALS/CAPITA > 0

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Chapter2Visualizing and Describing Categorical Data2-1127.Importance of wealth.a)India 76.1%-USA 45.3% = 30.8%, almost 31%b)The vertical axis on the display starts at 40% which makes the comparison between countries difficultand the areas disproportionate. For example, the India bar looks about 5-6 times as big as the USA barwhen in factthe actual values are not even twice as big.c)The display would be improved by starting the vertical axis at 0%, not 40%.d)e)The percentage of people who say that wealth is important to them is highest in China and India(over 70%),followed by France (close to 60%) and then the USA and U.K. where the percentageswere close to 45%.28.Importance of power.a)The percentages don’t add up to 100% so a pie chart is not appropriate. Showing the pie chartthree dimensionally on a slant violates theareaprinciple and makes it much more difficult tocompare fractions of the whole.b)A bar chart is more appropriate.40.00%45.00%50.00%55.00%60.00%65.00%70.00%75.00%80.00%ChinaFranceIndiaU.K.U.S.

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2-12Chapter2Visualizing and Describing Categorical Datac)The percentage of people who say that power is important to them is highest in India (over 75%),followed by China (close to 72%) and then France (almost 60%). The lowest percentages occur inUSA and the UK (both close to 45%).29.GEfinancials.a)These are column percentages because the column sums add up to 100% and the row percentagesadd up to more than 100%.b)A stacked barchart is appropriate.c)Over 50% of GE’s revenue comes Power, Aviation, and Healthcare,except in 2012, which had amajor drop in Aviation revenue and a major increase in Other. In a typical year, 45% of revenue isaccounted by Other sources.30.Realestate pricing.a)These are column percentages because the column sums add up to 100% and the row percentagesadd up to more than 100%.b)2.4%c)This cannot be determined. We are only given the percentages of size within each Price category.d)Small 61.5% + Med Small 30.4% = 91.9%.e)Larger houses appear to cost more. A stacked bar chart is shown below illustrating the changingconditional distributions.0%10%20%30%40%50%60%70%80%90%100%20152014201320122011PowerAviationHealthcareOther

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Chapter2Visualizing and Describing Categorical Data2-1331.Stock performance.a)45.1% (164+48)/470)b)34.9% (164)/470)c)5.3% (25/470)d)59.8% (48+233)/470)e)41.3% (164/397)f)65.8% 48/(48+25)g)Companies that reported a positive change ona single daywere more likely to report a negativechange for theyear than companies who reported a negative change ona single day.32.New product.a)4.0% (56/1415)b)34% (481/1415)c)3.7%(18/481)d)32.1% (18/56)e)Marginal Distributions–total % of the categories: Students 64.0%; Faculty/Staff 23.9%; Alumni4.0%; Town Residents 8.2%.f)Conditional Distributions–percentages forVery Likelycolumn: Students 66.5%; Faculty/Staff20.4%; Alumni 3.7%; Town Residents 9.4%.g)The likelihood to buy seems independent of campus group (compare percentages forVery Likelyin each category). However, there are more students, so focusing advertising in that group mayhave a greater impact on revenue.33.Foreclosures 2016.a)10.1% (203,108/2,020,354)b)33.4% (2,300,000/6,891,060)c)12.5% (575,378/4,599,817)d)Overall, the change was–71.0%. On a compound annual growth rate basis, this is–26.6% peryear.e)Answers may vary. Two things stand out: the numbers seem rounded for 2012 and not for theother years. Two numbers in 2014 and 2015 are identical.

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2-14Chapter2Visualizing and Describing Categorical Data34.Applfinancials.a)R&D %2014:4.2%(6,041,000/144,265,000);2016: 5.9%(10,045,000/171,300,000)b)Tax % 2015:10.5%(19,121,000/181,606,000);2016:9.2%(15,685,000/171,300,000)c)In absolute dollars, SG&A has increased,but because total expenses have increased, as apercentage of total expenses, SG&A has fallen slightly.d)e)35.Movie ratings.a)Conditional distribution (in percentages) of movie ratings for action films:R or NC-17PG-13PGGTotalAction44.1%52.9%2.9%0.0%100.0%b)Conditional distribution (in percentages) of movie ratings forPG-13films:201420152016Cost ofRevenue77.8%77.1%76.7%Research & Development4.2%4.4%5.9%Selling, General, & Administrative8.3%7.9%8.3%Income Tax Expense9.7%10.5%9.2%PG-13Action15.1%Comedy21.8%Drama51.3%Thriller/Suspense11.8%0%10%20%30%40%50%60%70%80%90%100%Cost of RevenueResearch &DevelopmentSelling, General, &AdministrativeIncome Tax Expense201420152016

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Chapter2Visualizing and Describing Categorical Data2-15c)Depending on what you want to emphasize, either segmented bar chart shown below isappropriate. Placing Genre on thex-axisemphasizes that Dramas are themost commonly madefilm type. Placing MPAA Rating on thex-axis show that R (or NC-17) movies are the mostcommonly made.020406080100120140160180ActionComedyDramaThriller/SuspenseR or NC-17PG-13PGG050100150200250R or NC-17PG-13PGGActionComedyDramaThriller/Suspense

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2-16Chapter2Visualizing and Describing Categorical Datad)GenreandRatingdo not appear to beindependent.It appears that it is more likely for aDrama or a Comedy to be rated PG than Action or Thriller. Similarly, Thriller/Suspensemovies are more likely to be rate R.36.CyberShopping.a)Conditional distribution (in percentages) of income distribution forthose who do NOT compareprices on theInternet:b)Conditional distribution (in percentages) of income distribution forthose who DO compare priceson the Internet:Under $30K31.4%(207/660)$30K-$50K17.4%(115/660)$50K-$75K20.3%(134/660)Over $75K30.9%(204/660)c)Barchart:d)Answers may vary.Comparison shopping is more common among those with higher incomes.37.MBAs.a)62.7% (168/268)b)62.8% (103/164)c)62.5% (65/104)d)The marginal distribution of origin: 23.9% from Asia; 1.9% from Europe; 7.8% fromLatinAmerica; 3.7% from the Middle East; 62.7% from North America.Under $30K36.6%(625/1708)$30K-$50K23.8%(406/1708)$50K-$75K15.2%(260/1708)Over $75K24.4%(417/1708)

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Chapter2Visualizing and Describing Categorical Data2-17e)The column percentages:Two-YrEveningTotalAsia/Pacific Rim18.9031.7323.88Europe3.050.001.87Latin America12.200.967.84Middle East/Africa3.054.813.73NorthAmerica62.8062.5062.69Total100.00100.00100.00f)They are not independent.For example, there is less than a 19% chance (31/164) that a randomlyselected Two-Year MBA student is an Asian/Pacific Rim student. However, there is more than a31% chance (33/104) that a randomly selected Evening MBA student is an Asian/Pacific Rimstudent. This is over a 50% increase in the likelihood that a student is an Asian/Pacific Rimstudent.In addition, the percentage from Latin America in Two-Year programs is 12.2% while forthos in the Evening programs is leass than 1%.Thus knowing the kind of MBA program doesaffect the likelihood of the origin of the MBA student.38.MBAs, part 2.a)32.1% (86/268)b)29.3% (48/164)c)36.5% (38/104)d)There seems to be a slightly higher percentage of Evening MBAs who are women. This may bebecause women haveother commitments during the day (such as work, family, etc.) that limittheir choices.39.Top producing movies.a)2.0% (135/6897)b)2.5% (18/716)c)2.0%(140/6897)d)20.0% (943/4,718)e)54.5.0% ((592+879+3)/2,703)f)More movies were unrated in the 2011-2015time period than the 2006-2010 period.However, of the movies that were rated, the distributions are similar. There are slightlymore R rated movies in the 2006-2010 time period but this could be because makers of Rrated movies chose instead to release them unrated in the later time period (2011-2015).40.Movie admissions2016.a)33.4% ((16.2+19.9)/108.1)b)56.7% ((5.4+7.2+8)/36.3)c)6.5% (7/108.1)d)14.9% (5.1/34.3)e)4.7% (5.1/108.1)f)Theconditional age distribution-each value is divided by the total forthat year:NC-17RPG-13PGGNot Rated2006-20100.15%33.11%20.80%9.87%2.13%33.94%2011-20150.16%30.36%19.64%8.40%1.81%39.63%

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2-18Chapter2Visualizing and Describing Categorical Data2-1112-1718-2425-3940-4950-5960+20168.5%14.9%19.8%22.0%9.1%11.6%14.0%20158.5%15.5%16.6%21.6%13.1%9.9%14.9%20147.2%14.7%18.7%18.9%15.2%11.2%14.1%The age distribution stayed fairly constant between thethree years. The largest percentage ofmovie goers are in the age groups 18-24 and 25-39 consistently. There seems to be a substantialdecline in the 40-49 age group and older. Other changes seem to more like random fluctuationsand not extreme.41.Tattoos.The study by the University of Texas Southwestern Medical Center provides evidence of anassociation between having a tattoo and contracting hepatitis C. Approximately 33% of the subjects who weretattooed in a commercial parlor had hepatitis C, comparedwith 13% of those tattooed elsewhere, and only 3.5%of those with no tattoo. If having a tattoo and having hepatitis C were independent, we would have expectedthese percentages to be roughly the same.42.Poverty and region 2015.The percentage of people living below poverty level in the four regions are:12.4,11.7, 15.3and 13.3, respectively. Although the rates are similar, there do seem to be higher rates inthe South and West than in theNortheast and Midwest.43.Being successful.a)51.4%((139+273)/802)b)Men are slightly higher. Young men: 54.3% ((163+346)/937)c)The distributions are similar, but slightly more men say that a high-paying job is “very” important, andslightly more women saythat a high-paying job is “somewhat” important.44.Minimum wage workers.a)20.3% (Count for 16-24 divided by Total Female: 7701/37,972)b)It can be seen from the side-by-side bar graph below that the proportion of female workers whowork at minimum wage or less is nearly twice that of men at every age group.0%10%20%30%40%50%60%70%80%90%100%Tattoo Done inCommercial ParlorTattoo DoneElsewhereNo TattooHas Hepatitis CNo Hepatitis C

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Chapter2Visualizing and Describing Categorical Data2-1945.Moviegoers and ethnicity.a)CaucasianHispanicAfrican-AmericanOtherPopulation66.0%(204.6/310)16.0%(49.6/310)12.0%(37.2/310)6.0%(18.6/310)Moviegoers63.0%(88.8/141)19.0%(26.8/141)12.0%(16.9/141)6.0%(8.5/141)Tickets56.0%(728/1300)26.0%(338/1300)11.0%(143/1300)7.0%(91/1300)b)The distributions of moviegoers are quite similar to the population as a whole, but Hispanicsappear to buy proportionally more tickets and Caucasians fewer. Hispanicsappear to goto themovies more often, on average, than Caucasians.46.Department store.a)Low 20.0%; Moderate 48.9%; High 31.0%.b)Under 30: Low 27.6%; Moderate 49.0%; High 23.5%30-49: Low 20.7%; Moderate 50.8%; High 28.5%Over 50: Low 15.7%; Moderate 47.2%; High 37.1%-0.020.040.060.080.100.1216-2425-3435-4445-5455-6465+MenWomen

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2-20Chapter2Visualizing and Describing Categorical Datac)d)As age increases, the percentage of customers reporting a high frequency of shopping increases, andthe percentage who report a low frequency of shopping decreases.e)No. Anassociation between two variables does not imply a cause-and-effect relationship.47.Success II.Needs changesa)53.0%b)Number of 18-34 yr oldswho think being successful is one of the most important things=44.7%48.Income and pets.a)No, the incomedistributions of households by pet ownership wouldn’t be expected to be the same.Caring for a horse is much more expensive, generally, than caring for a dog, cat, or bird.Households with horses as pets would be expected to be more common in the higher incomecategories.b)Column percentages (add up to 100%).c)No. Among horse owners, there are relatively fewer households in the lowest income bracket andrelatively more households in the highest income bracket. In the middle income ranges, thepercentages are about the same for each of the different types of pets.49.Insurance company, part 2.a)The marginal totals were added. 160 of 1300 or 12.3% had a delayed discharge.b)Major surgery patients were delayed 15.3% of the time. Minor surgery patients were delayed 6.7%of the time.c)Large Hospital had a delay rate of 13%. SmallHospital had a delay rate of 10%. The smallhospital has the lower overall rate of delayed discharge.d)Large Hospital: Major Surgery 15% and Minor Surgery 5%.Small Hospital: Major Surgery 20% and Minor Surgery 8%.e)Yes, while the overall rate of delayed discharge is lower for the small hospital, the large hospitaldid better withbothmajor and minor surgery.f)The small hospital performs a higher percentage of minor surgeries than major surgeries. 250 of300 surgeries at the small hospital were minor(83%). Only 200 of the large hospital’s 1000surgeries were minor (20%). Minor surgery had a lower delay rate than major surgery (6.7% to15.3%), so the small hospital’s overall rate was artificially inflated. The larger hospital is the betterhospital when comparing discharge delay rates.Large HospitalSmall HospitalTotalMajor surgery120 of 80010 of 50130 of 850Minor surgery10 of 20020 of 25030 of 450Total130 of 100030 of 300160 of 1300

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