Stats: Modeling the World, 5th Edition Solution Manual

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SOLUTIONSMANUALADAMYANKAYSTATSMODELING THEWORLDFIFTHEDITIONDavid E. BockIthaca High School (Retired)Floyd BullardNorth Carolina School of Science and MathematicsPaul F. VellemanCornell UniversityRichard D. De VeauxWilliams College

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ContentsPart IExploring and Understanding DataChapter 1Stats Starts Here1Chapter 2Displaying and Describing Categorical Data5Chapter 3Displaying and SummarizingQuantitative Data20Chapter 4Understanding and ComparingDistributions39Chapter 5The Standard Deviation as a Ruler andthe Normal Model55Review of Part IExploring and Understanding Data74Part IIExploring Relationships Between VariablesChapter 6Scatterplots, Association, and Correlation102Chapter 7Linear Regression113Chapter 8Regression Wisdom138Chapter 9Re-expressing Data: Get It Straight!157Review of Part IIExploring Relationships Between Variables168Part IIIGathering DataChapter 10Understanding Randomness194Chapter 11Sample Surveys204Chapter 12Experiments215Review of Part IIIGathering Data233Part IVRandomness and ProbabilityChapter 13From Randomness to Probability249Chapter 14Probability Rules!262Chapter 15Random Variables284Chapter 16Probability Models305Review of Part IVRandomness and Probability334

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Part VFrom the Data at Hand to the World at LargeChapter 17Sampling Distribution Models358Chapter 18Confidence Intervals for Proportions392Chapter 19Testing Hypotheses About Proportions408Chapter 20More About Tests and Intervals427Chapter 21Comparing Two Proportions444Review of Part VFrom the Data at Hand to the World at Large469Part VILearning About the WorldChapter 22Inferences About Means497Chapter 23Comparing Means523Chapter 24Paired Samples and Blocks553Review of Part VILearning About the World573Part VII Inference When Variables are RelatedChapter 25Comparing Counts611Chapter 26Inferences for Regression642Review of Part VIIInference When Variables are Related669Chapter 27Analysis of Variance707Chapter 28Multiple Regression718

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Chapter 1Stats Starts Here1Chapter 1 – Stats Starts Here1.Voters.The response, party affiliation, is a categorical variable.2.Job growth.The response, change in workforce size, is a categorical variable.3.Medicine.The company is measuring minutes, a quantitative variable.4.Stress.The researcher is measuring heart rate, a quantitative variable.5.The news.Answers will vary.6.The Internet.Answers will vary.7.Bicycle and pedestrian safety.Who –pedestrians and bicyclists killed or severelyinjured in New York City between 2010 and 2014.What –proportion of pedestriansand bicyclists killed or injured by left-turning and right-turning vehicles.Populationof interest–Answers may vary. Perhaps: All pedestrians and bicyclists killed orseverely injured in New York City between 2010 and 2014orall pedestrians andbicyclists killed or severely injured in New York City in any yearorall pedestriansand bicyclists killed or severely injured in major U.S. cities. Discuss with studentswhy these and other solutions may be problematic.8.Investments.Who– 30 companies with similar retirement plans.What– 401(k)employee participation rates.Population of interest –All companies with similarretirement plans.9.Fake news.Who –Middle school, high school, and college students in 12 states.What –Ability to evaluate the quality of information found in different onlineresources.Population of interest –All U.S middle school, high school, and collegestudents.10.Biological instinct.Who –40 undergraduate women.What –Whether or not thewomen could identify the sexual orientation of men based on a picture.Population ofinterest–All women.11. Blindness.Who –24 patients.What –Whether or not stem cell therapy was effectivein treating Stargardt’s disease and/or dry age-related macular degeneration.Population of interest –All people with these eye conditions.12. Molten iron.Who– 10 castings at Cleveland Casting.What– The pouringtemperature (in degrees Fahrenheit) of molten iron.Population of interest –Allcastings at Cleveland Casting.

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2Part IExploring and Understanding Data13. Weighing bears.Who– 54 bears.What– Weight, neck size, length (no specifiedunits), and sex.When– Not specified.Where– Not specified.Why- Since bears aredifficult to weigh, the researchers hope to use the relationships between weight,neck size, length, and sex of bears to estimate the weight of bears, given the other,more observable features of the bear.How– Researchers collected data on 54 bears they were able to catch.Variables–There are 4 variables: weight, neck size, and length are quantitative variables, andsex is a categorical variable. No units are specified for the quantitative variables.Concerns –The researchers are (obviously!) only able to collect data from bears theywere able to catch. This method is a good one, as long as the researchers believe thebears caught are representative of all bears, in regard to the relationships betweenweight, neck size, length, and sex.14. Schools.Who– Students.What– Age (probably in years, though perhaps in yearsand months), race or ethnicity, number of absences, grade level, reading score, mathscore, and disabilities/special needs.When– This information must be kept current.Where– Not specified.Why– Keeping this information is a state requirement.How–The information is collected and stored as part of school records.Variables –Thereare seven variables. Race or ethnicity, grade level, and disabilities/special needs arecategorical variables. Number of absences, age, reading test score, and math testscore are quantitative variables.Concerns –What tests are used to measure readingand math ability, and what are the units of measure for the tests?15. Arby’s menu.Who– Arby’s sandwiches.What– type of meat, number of calories(in calories), and serving size (in ounces).When– Not specified.Where– Arby’srestaurants.Why– These data might be used to assess the nutritional value of thedifferent sandwiches.How– Information was gathered from each of the sandwicheson the menu at Arby’s, resulting in a census.Variables– There are three variables.Number of calories and serving size are quantitative variables, and type of meat is acategorical variable.16. Party and the environment.Who –American voters.What –Gender, age (in years),race, party affiliation, education, whether or not the person was “worried a greatdeal” about climate change, air pollution, and pollution of waterways.When– 2017.Where –United States.Why –The information was gathered for presentation in aGallup public opinion poll.How –Poll.Variables –There are eight variables.Gender, race, party affiliation, education, whether or not the person was “worried agreat deal” about climate change, air pollution, and pollution of waterways arecategorical variables; age is a quantitative variable.17. Babies.Who –882 births.What –Mother’s age (in years), length of pregnancy (inweeks), type of birth (caesarean, induced, or natural), level of prenatal care (none,minimal, or adequate), birth weight of baby (unit of measurement not specified,gender of baby (male or female), and baby’s health problems (none, minor, major).When –1998-2000.Where –Large city hospital.Why –Researchers were

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Chapter 1Stats Starts Here3investigating the impact of prenatal care on newborn health.How –It is notspecifically stated.Variables –There are seven variables. Type of birth, level ofprenatal care, gender of baby, and baby’s health problems are categorical variables;mother’s age, length of pregnancy, and birth weight of baby are quantitativevariables.18. Flowers.Who– 385 species of flowers for 47 years. 385(47) = 18,095 cases.What–Date of first flowering (in days).When– An unspecified 47 year period.Where–Southern England.Why– The researchers believe that this indicates a warming ofthe overall climate.How– Not specified.Variables– Date of first flowering is aquantitative variable. The number of years, 47, is also a variable.19. Herbal medicine.Who– Patients.What– Herbal cold remedy or sugar solution,and cold severity on a scale of 0-5.When– Not specified.Where– Majorpharmaceutical firm.Why– Scientists were testing the efficacy of an herbalcompound on the severity of the common cold.How– The scientists conducted anexperiment.Variables– There are two variables. Type of treatment (herbal or sugarsolution) is a categorical variable, and severity rating is a quantitative variable. Thesubjectivity of “cold severity” is a concern that should be raised about this study.20. Vineyards.Who –Vineyards.What –Size of vineyard (in acres), number of years inexistence, state, varieties of grapes grown, average case price (in dollars), gross sales(probably in dollars), and percent profit.When –Not specified.Where –UnitedStates.Why –Business analysts hoped to provide information that would be helpfulto producers of American grapes.How –Notspecified.Variables –There are sevenvariables. State and variety of grapes grown are categorical variables; size ofvineyard, number of years in existence, average case price, gross sales, and percentprofit are quantitative variables.21. Streams.Who –Streams.What– A number of variables including: name of stream,substrate of the stream (limestone, shale, or mixed), acidity of the water (measuredin pH), temperature (in degrees Celsius), and BCI (unknown units).When –Notspecified.Where –Upstate New York.Why –Research is conducted for an ecologyclass.How –Not specified.Variables –There are five variables. Name and substrateof the stream are categorical variables; acidity, temperature, and BCI are quantitativevariables.22. Fuel economy.Who –Every model of automobile.What –Vehicle manufacturer,vehicle type, weight (probably in pounds), horsepower (in horsepower), and gasmileage (in miles per gallon) for city and highway driving.When –This informationis collected currently.Where –United States.Why –The Environmental ProtectionAgency uses the information to track fuel economy of vehicles.How –The data iscollected from the manufacturer of each model.Variables –There are six variables.Manufacturer and type of car are categorical variables; weight, horsepower, citymileage, and highway mileage are quantitative variables.

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4Part IExploring and Understanding Data23. Refrigerators.Who –148 models of French door style refrigerators.What –Brand,price (probably in dollars), temperature performance, temperature uniformity,energy efficiency, noise, ease of use (the five previous variables are measured asExcellent, Very Good, Good, Fair, or Poor), number of doors, capacity (cu. ft.),exterior height (in.), exterior width (in.), and exterior depth (in.).When –2017.Where –Not stated.Why –The information was compiled to provide information tothe readers ofConsumer Reports.How –Not specified.Variables –There are 11variables. Brand, temperature performance, temperature uniformity, energyefficiency, noise, and ease of use are categorical variables; price, number of doors,capacity, exterior height, exterior width, and exterior depth are quantitativevariables.24. Walking in circles.Who –32 people.What –Sex, height, handedness, the numberof yards walked before going out of bounds, and the side of the field on which theperson walked out of bounds.When –Not specified.Where –Not specified.Why –The researcher was interested in whether people naturally walk in circles when lost.How –Data were collected by observing the people on the field, as well as bymeasuring and asking the participants.Variables –There are 5 variables. Sex,handedness, and side of the field are categorical variables; height and number ofyards walked are quantitative variables.25.Kentucky Derby 2016.Who –Kentucky Derby races.What –Year, winner, jockey,trainer, owner, and time (in minutes, seconds, and hundredths of a second.When –1875 – 2016.Where –Churchill Downs, Louisville, Kentucky.Why –Not specified.How –Official statistics are kept for the race each year.Variables –There are 6variables. Winner, jockey, trainer and owner are categorical variables; year and timeare quantitative variables.26. Indy 2016.Who –Indy 500 races.What –Year, winner, time (in minutes, seconds,and hundredths of a second), and average speed (in miles per hour).When –1911 –2016.Where –Indianapolis Motor Speedway.Why –Not specified.How– Officialstatistics are kept for the race every year.Variables –There are 4 variables. Winneris a categorical variable, while year, time, and average speed are quantitativevariables.

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Chapter 2Displaying and Describing Categorical Data5Chapter 2 – Displaying and Describing Categorical Data1.Graphs in the news.Answers will vary.2.Graphs in the news II.Answers will vary.3.Tables in the news.Answers will vary.4.Tables in the news II.Answers will vary.5.Movie genres.a)A pie chart seems appropriate from the movie genre data. Each movie has onlyone genre, and the 891 movies constitute a “whole”.b)“Other” is the least common genre. It has the smallest region in the chart.6.Movie ratings.a)A pie chart seems appropriate for the movie rating data. Each movie has onlyone rating, and the 891 movies constitute a “whole”.b)The most common rating is R. It has the largest region on the chart.7.Movie genres again.a)Thriller/Suspense films were more common than Adventure films. The bar forThriller/Suspense is taller than the bar for Adventure.b)This is easier to see on the bar chart. The percentages are so close that thedifference is nearly indistinguishable in the pie chart. Also, the bar chart isorganized by height while the pie chart is not, making it difficult to comparegenres with areas similar in proportion.8.Movie ratings again.a)The least common rating was NC-17. It has the shortest bar.b)While it is easy in both the pie chart and the bar chart, it may be easier in the piechart. In the pie chart, ratings are ordered clockwise by increasing area while inthe bar chart, G and NC-17 are inconsistent with an increasing order.9.Movie ratings.i. C (This chart has 4 ratings and the proportion of G ratings is smallest.)ii. A (This chart has 4 ratings and a slightly higher proportion of G ratings.)iii. D (This chart has 3 ratings with PG more common than R.)iv. B (This chart has 3 ratings with PG and R roughly equally as common.)10. Marriage in decline.i. D (This bar and pie chart are the only ones for which Bad Thing and NoDifference are not roughly equally common)

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6Part IExploring and Understanding Dataii. A (Bad Thing and No Difference are roughly equal, while Don’t Know/NoResponse is noticeably the least frequent response)iii. B or C (These charts are indistinguishable.)iv. B or C (These charts are indistinguishable.)11.Magnet schools.There were 1,755 qualified applicants for the Houston Independent SchoolDistrict’s magnet schools program. Approximately 53% were accepted, 17%were wait-listed, and the other 30% were turned away for lack of space.12. Magnet schools again.There were 1,755 qualified applicants for the Houston Independent SchoolDistrict’s magnet schools program. Approximately 29.5% were Black orHispanic, 16.6% were Asian, and 53.9% were white.13. Causes of death 2014.a)Yes, it is reasonable toassume that heart orlung diseases causedapproximately 29% ofU.S. deaths in 2014,since there is nopossibility for overlap.Each person couldonly have one cause ofdeath.b)Since the percentageslisted add up to 61.9%,other causes mustaccount for 38.1% ofUS deaths.c)A bar chart is a good choice (with the inclusion of the “Other” category). Sincecauses of US deaths represent parts of a whole, a pie chart would also be a gooddisplay.

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Chapter 2Displaying and Describing Categorical Data714. Plane crashes.a)As long as each plane crash had only one cause, it would be reasonable toassume that weather or mechanical failures were the causes of about 20% ofrecent plane crashes.b)Since the percentages listed add up to 71%, other causes (not determined) mustaccount for 29% of recent plane crashes.c)A relative frequency bar chart is a good choice. A pie chart would also be a gooddisplay, as long as each plane crash has only one cause.15. Oil spills as of 2016.a)Grounding, accounting for 150 spills, is the most frequent cause of oil spillage forthese 460 spills. A substantial number of spills, 136, were caused by collision.Less prevalent causes of oil spillage in descending order of frequency were hullfailures, other/unknown causes, fire/explosions, and equipment failure.b)If being able to differentiate between these close counts is required, use the barchart. Since each spill only has one cause, the pie chart is also acceptable as adisplay, but it’s difficult to tell whether, for example, there is a greaterpercentage of spills caused by fire/explosions or hull failure. If you want toshowcase the causes of oil spills as a fraction of all 460 spills, use the pie chart.16. Winter Olympics 2016.a)There are too many categories to construct an appropriate display. In a bar chart,there are too many bars. In a pie chart, there are too many slices. In each case,we run into difficulty trying to display those countries that didn’t win manymedals.

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8Part IExploring and Understanding Datab)Perhaps we are primarily interested in countries that won many medals. Wemight choose to combine all countries that won fewer than 6 medals into a singlecategory. This will make our chart easier to read. We are probably interested innumber of medals won, rather than percentage of total medals won, so we’ll usea bar chart. A bar chart is also better for comparisons.17. Global warming.Perhaps the most obvious error is that the percentages in the pie chart add up to141%, when they should, of course, add up to 100%. This means that eachindividual region and any resulting sums will occupy less area of the displaythan their percentages imply. Furthermore, the three-dimensional perspectiveview distorts the regions in the graph, violating the area principle. The regionscorresponding to “Global warming isn’t happening” and “Can’t reduce globalwarming even if it is happening” should be the same size, at 25% of respondents.However, the “Global warming isn’t happening” region looks bigger. Alwaysuse simple, two-dimensional graphs.18. Modalities.a) The bars have false depth, which can be misleading. This is a bar chart, so thebars should have space between them.b) Since each trainer was asked to list 3 modalities, the expected sum should be300% rather than 100%.19. Teen smokers.According to the Monitoring the Future study, teen smoking brand preferencesdiffer somewhat by region. Although Marlboro is the most popular brand ineach region, with about 58% of teen smokers preferring this brand in each region,teen smokers from the South prefer Newports at a higher percentage than teensmokers from the West, 22.5% to approximately 10%, respectively. Camels aremore popular in the West, with 9.5% of teen smokers preferring this brand,compared to only 3.3% in the South. Teen smokers in the West are also morelikely to have to particular brand than teen smokers in the South. 12.9% of teensmokers in the West have no particular brand, compared to only 6.7% in theSouth. Both regions have 9% of teen smokers that prefer one of over 20 otherbrands.20. Handguns.76% of handguns involved in Milwaukee buyback programs are small caliber,while only 20.3% of homicides are committed with small caliber handguns.Along the same lines, only 19.3% of buyback handguns are of medium caliber,while 54.7% of homicides involve medium caliber handguns. A similar disparityis seen in large caliber handguns. Only 2.1% of buyback handguns are largecaliber, but this caliber is used in 10.8% of homicides. Finally, 2.2% of buyback

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Chapter 2Displaying and Describing Categorical Data9handguns are of other calibers, while 14.2% of homicides are committed withhandguns of other calibers. Generally, the handguns that are involved inbuyback programs are not the same caliber as handguns used in homicides inMilwaukee.21. Movie genres and ratings.a)452 of these films were rated R. 452/1,529≈29.56%b)124 of these films were R-rated comedies. 124/1,529≈8.1%c)124 of the 452 R-rated films were comedies. 124/452≈27.43%d)124 of the 312 comedies were R-rated. 124/312≈39.74%22. Not the labor force.a)2207 of the unemployed population were available to work now. 2207/12,872≈17.1%b)1,048 of the unemployed population were available to work now and aged 25 to54 years. 1,048/12,872≈8.14%c)208 of 4,158 unemployed 16-24 year olds were in school or training. 208/4,158≈5%d)4,158 of the unemployed population were aged 16-24 years. 4,158/12,872≈32.3%23. Seniors.A table withmarginal totals isto the right.a)268 seniorswere white.268/325≈82.5%b)42 seniors areplanning to attend a 2-year college. 42/325≈13%c)36 seniors are white and planning to attend 2-year colleges. 36/325≈11.1%d)36 of the 268 white seniors are planning to attend 2-year colleges. 36/268≈13.4%e)There are 42 graduates planning to attend 2-year colleges. 36 are white. 36/42≈85.7%24. Politics.a)There are 192 students taking Intro Stats. Of those, 115 are male. 115/192≈59.9%.PlansWhiteMinorityTOTAL4-year college198442422-year college36642Military415Employment14317Other16319TOTAL26857325

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10Part IExploring and Understanding Datab)27 students in the course consider themselves to be “Conservative”. 27/192≈14%.c)There are 115 males taking Intro Stats. Of those, 21 consider themselves to be“Conservative”. 21/115≈18.26%.d)21 of the students in the course are males who consider themselves to be“Conservative”. 21/192≈10.94%25. More about seniors.a)For white students, 73.9% plan to attend a 4-year college, 13.4% plan to attend a2-year college, 1.5% plan on the military, 5.2% plan to be employed, and 6.0%have other plans.b)For minority students, 77.2% plan to attend a 4-year college, 10.5% plan to attenda 2-year college, 1.8% plan on the military, 5.3% plan to be employed, and 5.3%have other plans.c)A segmented barchart is a gooddisplay of thesedata:d)The conditional distributions of plans for Whites and Minorities are similar:White – 74% 4-year college, 13% 2-year college, 2% military, 5% employment, 6%other.Minority – 77% 4-year college, 11% 2-year college, 2% military, 5% employment,5% other.Caution should be used with the percentages for Minority graduates, because thetotal is so small. Each graduate is almost 2%. Still, the conditional distributionsof plans are essentially the same for the two groups. There is little evidence of anassociation between race and plans for after graduation.Post High School Plans4-year college4-year college2-year college2-year collegeOtherOtherEmploymentEmployment0%10%20%30%40%50%60%70%80%90%100%WhiteMinorityMilitary

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Chapter 2Displaying and Describing Categorical Data1126. Politics revisited.a)The females in this coursewere 45.5% Liberal, 46.8%Moderate, and 7.8%Conservative.b)The males in this course were43.5% Liberal, 38.3%Moderate, and 18.3%Conservative.c)A segmented bar chartcomparing the distributions isat the right.d)Politics and sex do not appear to be independent in this course. Although thepercentage of liberals was roughly the same for each sex, females had a greaterpercentage of moderates and a lower percentage of conservatives than males.27. Magnet schools revisited.a)There were 1,755 qualified applicants to the Houston Independent SchoolDistrict’s magnet schools program. Of those, 292 were Asian. 292/1,755≈16.6%b)There were 931 students accepted to the magnet schools program. Of those, 110,were Asian. 110/931≈11.8%.c)There were 292 Asian applicants. Of those, 110 were accepted. 110/292≈37.7%.d)There were 1,755 total applicants. Of those, 931 were accepted. 931/1,755≈53%.28. More politics.a)0%10%20%30%40%50%60%70%80%90%100%LibModConDistribution of Sex Across Political CategoriesMMMFFFPercentPoliticsPolitics of an Intro Stats CourseLiberalLiberalModerateModerateConservativeConservative0%10%20%30%40%50%60%70%80%90%100%FemaleMalePercent

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12Part IExploring and Understanding Datab)The percentage of males and females varies across political categories. Thepercentage of self-identified Liberals and Moderates who are female is abouttwice the percentage of Conservatives who are female. This suggests thatsexandpoliticsare not independent.29. Back to school.There were 1,755 qualified applicants for admission to the magnet schoolsprogram. 53% were accepted, 17% were wait-listed, and the other 30% wereturned away. While the overall acceptance rate was 53%, 93.8% of Blacks andHispanics were accepted, compared to only 37.7% of Asians, and 35.5% ofwhites. Overall, 29.5% of applicants were Black or Hispanics, but only 6% ofthose turned away were Black or Hispanic. Asians accounted for 16.6% ofapplicants, but 25.3% of those turned away. It appears that the admissionsdecisions were not independent of the applicant’s ethnicity.30. Cars.a)In order to get percentages, first we needtotals. Here is the same table, with rowand column totals. Foreign cars aredefined as non-American. There are45+102=147 non-American cars or147/359≈40.95%.b)There are 212 American cars of which 107 or 107/212≈50.47% were owned bystudents.c)There are 195 students of whom 107 or 107/195≈54.87% owned American cars.d)The marginal distribution of Origin is displayed inthe third column of the table at the right: 59%American, 13% European, and 28% Asian.e)The conditional distribution of Origin for Studentsis: 54.8% (107 of 195) American, 17% (33 of 195) European, and 28% (55 of 195)Asian.The conditional distribution of Origin for Staff is:64% (105 of 164) American, 7% (12 of 164) European, and 29% (47 of 164) Asian.DriverOriginStudentStaffTotalAmerican107105212European331245Asian5547102Total195164359OriginTotalsAmerican212 (59%)European45 (13%)Asian102 (28%)Total359

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