Solution Manual for Fundamentals of Statistics, 6th Edition

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’SSOLUTIONSMANUALDIACRITECHFUNDAMENTALS OFSTATISTICS:INFORMEDDECISIONSUSINGDATASIXTHEDITIONMichael Sullivan, IIIJoliet Junior College

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Table of ContentsPrefaceChapter 1Data Collection1.1Introduction to the Practice of Statistics ............................................................................................................. 11.2Observational Studies versus Designed Experiments ......................................................................................... 41.3Simple Random Sampling .................................................................................................................................. 71.4Other Effective Sampling Methods .................................................................................................................... 91.5Bias in Sampling............................................................................................................................................... 111.6The Design of Experiments .............................................................................................................................. 14Chapter 1 Review Exercises........................................................................................................................................ 21Chapter 1 Test ............................................................................................................................................................. 24Case Study: Chrysalises for Cash................................................................................................................................ 26Chapter 2Summarizing Data in Tables and Graphs2.1Organizing Qualitative Data ............................................................................................................................. 282.2Organizing Quantitative Data ........................................................................................................................... 382.3Graphical Misrepresentations of Data .............................................................................................................. 51Chapter 2 Review Exercises........................................................................................................................................ 53Chapter 2 Test ............................................................................................................................................................. 58Case Study: The Day the Sky Roared.......................................................................................................................... 62Chapter 3Numerically Summarizing Data3.1Measures of Central Tendency ......................................................................................................................... 653.2Measures of Dispersion .................................................................................................................................... 723.3Measures of Central Tendency and Dispersion from Grouped Data ................................................................ 893.4Measures of Position and Outliers .................................................................................................................... 993.5The Five-Number Summary and Boxplots ..................................................................................................... 106Chapter 3 Review Exercises...................................................................................................................................... 117Chapter 3 Test ........................................................................................................................................................... 123Case Study: Who Was “A Mourner”? ....................................................................................................................... 126Chapter 4Describing the Relation between Two Variables4.1Scatter Diagrams and Correlation................................................................................................................... 1284.2Least-Squares Regression ............................................................................................................................... 1494.3The Coefficient of Determination................................................................................................................... 1614.4Contingency Tables and Association.............................................................................................................. 165Chapter 4 Review Exercises...................................................................................................................................... 178Chapter 4 Test ........................................................................................................................................................... 184Case Study: Thomas Malthus, Population, and Subsistence ..................................................................................... 187Chapter 5Probability5.1Probability Rules ............................................................................................................................................ 1895.2The Addition Rule and Complements............................................................................................................. 1985.3Independence and the Multiplication Rule ..................................................................................................... 2065.4Conditional Probability and the General Multiplication Rule ........................................................................ 2105.5Counting Techniques ...................................................................................................................................... 2175.6Simulating Probability Experiments ............................................................................................................... 2215.7Putting It Together: Which Method Do I Use?............................................................................................... 223Chapter 5 Review Exercises...................................................................................................................................... 226Chapter 5 Test ........................................................................................................................................................... 229Case Study: The Case of the Body in the Bag........................................................................................................... 230

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Chapter 6Discrete Probability Distributions6.1Discrete Random Variables.............................................................................................................................2336.2The Binomial Probability Distribution............................................................................................................243Chapter 6 Review Exercises ......................................................................................................................................258Chapter 6 Test............................................................................................................................................................261Case Study: The Voyage of the St. Andrew ..............................................................................................................264Chapter 7The Normal Probability Distribution7.1Properties of the Normal Distribution.............................................................................................................2667.2Applications of the Normal Distribution.........................................................................................................2697.3Assessing Normality .......................................................................................................................................2897.4The Normal Approximation to the Binomial Probability Distribution ...........................................................292Chapter 7 Review Exercises ......................................................................................................................................296Chapter 7 Test............................................................................................................................................................301Case Study: A Tale of Blood Chemistry....................................................................................................................304Chapter 8Sampling Distributions8.1Distribution of the Sample Mean ....................................................................................................................3068.2Distribution of the Sample Proportion ............................................................................................................319Chapter 8 Review Exercises ......................................................................................................................................325Chapter 8 Test............................................................................................................................................................328Case Study: Sampling Distribution of the Median ....................................................................................................330Chapter 9Estimating the Value of a Parameter Using Confidence Intervals9.1Estimating a Population Proportion ................................................................................................................3369.2Estimating a Population Mean ........................................................................................................................3439.3Putting It Together: Which Method Do I Use? ...............................................................................................3539.4Estimating a Population Standard Deviation...................................................................................................3599.5Estimating with Bootstrapping........................................................................................................................361Chapter 9 Review Exercises ......................................................................................................................................366Chapter 9 Test............................................................................................................................................................370Case Study: Fire-Safe Cigarettes ...............................................................................................................................372Chapter 10 Hypothesis Tests Regarding a Parameter10.1The Language of Hypothesis Testing..............................................................................................................37410.2Hypothesis Tests for a Population Proportion.................................................................................................37710.2A Using Simulation to Perform Hypothesis Tests on a Population Proportion ..................................................38810.2B Hypothesis Tests for a Population Proportion Using the Normal Model........................................................39810.3Hypothesis Tests for a Population Mean.........................................................................................................40810.3A Using Simulation and the Bootstrap to Perform Hypothesis Tests on a Population Mean .............................41910.4Putting It Together: Which Method Do I Use? ...............................................................................................42610.5Hypothesis Tests for a Population Standard Deviation...................................................................................430Chapter 10 Review Exercises ....................................................................................................................................434Chapter 10 Test..........................................................................................................................................................438Case Study: How Old Is Stonehenge? .......................................................................................................................439

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Chapter 11 Inference on Two Population Parameters11.1Inference about Two Population Proportions ................................................................................................. 44211.1A Using Randomization Techniques to Compare Two Proportions................................................................... 45711.2Inference about Two Means: Dependent Samples.......................................................................................... 46511.2A Using Bootstrapping to Conduct Inference on Two Dependent Means.......................................................... 47711.3Inference about Two Means: Independent Samples ....................................................................................... 48411.3A Using Randomization Techniques to Compare Two Independent Means ...................................................... 49811.4Putting It Together: Which Method Do I Use?............................................................................................... 50211.5Inference about Two Populations Standard Deviations .................................................................................. 515Chapter 11 Review Exercises .................................................................................................................................... 520Chapter 11 Test ......................................................................................................................................................... 525Case Study: Control in the Design of an Experiment ................................................................................................ 531Chapter 12 Additional Inferential Methods12.1Goodness-of-Fit Test ...................................................................................................................................... 53312.2Tests for Independence and the Homogeneity of Proportions ........................................................................ 54412.3Testing the Significance of the Least-Squares Regression Model.................................................................. 56612.3A Using Randomization Techniques on the Slope of the Least-Squares Regression Line................................. 57112.4Confidence and Prediction Intervals............................................................................................................... 577Chapter 12 Review Exercises .................................................................................................................................... 583Chapter 12 Test ......................................................................................................................................................... 590Case Study: Feeling Lucky? Well, Are You?............................................................................................................ 597Appendix BB.1Lines ............................................................................................................................................................... 600B.2Inference about Two Population Proportions: Dependent Samples................................................................ 608B.3Comparing Three or More Means (One-Way Analysis of Variance) ............................................................ 611

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Chapter 1Data CollectionSection 1.11.(a)III. Statistics is the science of collecting,organizing, summarizing, and analyzinginformation in order to draw conclusionsand answer questions. It is also aboutproviding a measure of confidence in anyconclusions.(b)VIII. The population is the entire group ofindividuals to be studied.(c)IV. The sample is a subset of the group ofindividuals that is being studied.(d)VII. The parameter is a numericalsummary of a population.(e)I. The statistic is the numerical summaryof a sample.(f)VI. The individual is a person or objectthat is a member of the group beingstudied.(g)II. Descriptive statistics involvesorganizing and summarizing data throughtables, graphs, and numerical summaries.(h)V. Inferential statistics uses methods thattake results from a sample and extendsthem to the population, and measures thereliability of the result.2.(a)V. A discrete variable has either a finitenumber of possible values or countablenumber of possible values. The values ofthese variables typically result fromcounting.(b)IV. Data are information that describecharacteristics of an individual.(c)VI. A continuous variable has an infinitenumber of possible values that are notcountable. The values of these variablestypically result from measurement.(d)II. A qualitative variable allows forclassification of individuals based onsome attribute or characteristic.(e)I. A quantitative variable providesnumerical measures of individuals. Themeasures can be added or subtracted, andprovide meaningful results.(f)III. A variable is the characteristics of theindividuals within the population.3.18% is a parameter because it describes apopulation (all of the governors).4.72% is a parameter because it describes apopulation (the entire class).5.32% is a statistic because it describes a sample(the high school students surveyed).6.13.3% is a statistic because it describes asample (the 12th graders surveyed).7.0.366 is a parameter because it describes apopulation (all of Ty Cobb’s at-bats).8.43.92 hours is a parameter because it describesa population (all the men who have walked onthe moon).9.23% is a statistic because it describes a sample(the 6076 adults studied).10.44% is a statistic because it describes a sample(the 100 adults interviewed).11.Qualitative12.Quantitative13.Quantitative14.Qualitative15.Quantitative16.Quantitative17.Qualitative18.Qualitative19.Discrete20.Continuous21.Continuous22.Discrete23.Continuous24.Continuous25.Discrete26.Continuous27.Nominal28.Ordinal29.Ratio30.Interval31.Ordinal32.Nominal33.Ratio34.Interval35.The population consists of all teenagers 13 to17 years old who live in the United States.The sample consists of the 1028 teenagers 13to 17 years old who were contacted by theGallup Organization.

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2Chapter 1:Data Collection36.The population consists of all bottles of Coca-Cola filled by that particular machine onOctober 15. The sample consists of the50 bottles of Coca-Cola that were selected bythe quality control manager.37.The population consists of all of the soybeanplants in this farmer’s crop. The sampleconsists of the 100 soybean plants that wereselected by the farmer.38.The population consists of all householdswithin the United States. The sample consistsof the 50,000 households that are surveyed bythe U.S. Census Bureau.39.The population consists of all women 27 to44 years of age with hypertension. The sampleconsists of the 7373 women 27 to 44 years ofage with hypertension who were included inthe study.40.The population consists of all full-timestudents enrolled at this large communitycollege. The sample consists of the 128 full-time students who were surveyed by theadministration.41.Individuals: Alabama, Colorado, Indiana,North Carolina, Wisconsin.Variables: Minimum age for driver’s license(unrestricted); mandatory belt use seatingpositions, maximum allowable speed limit(rural interstate) in 2011.Data for minimum age for driver’s license: 17,17, 18, 16, 18;Data for mandatory belt use seating positions:front, front, all, all, all;Data for maximum allowable speed limit(rural interstate) 2011: 70, 75, 70, 70, 65(mph.)The variableminimum age for driver’s licenseis continuous; the variablemandatory belt useseating positionsis qualitative; the variablemaximum allowable speed limit (ruralinterstate) 2011is continuous (although onlydiscrete values are typically chosen for speedlimits.)42.Individuals: 3 Series, 5 Series, 6 Series,7 Series, X3, Z4 RoadsterVariables: Body Style, Weight (lb), Numberof SeatsData for body style: Coupe, Sedan,Convertible, Sedan, Sport utility, Coupe;Data for weight: 3362, 4056, 4277, 4564,4012, 3505 (lb);Data for number of seats: 4, 5, 4, 5, 5, 2. Thevariablebody styleis qualitative; the variableweightis continuous; the variablenumber ofseatsis discrete.43.(a)The research objective is to determine ifadolescents who smoke have a lower IQthan nonsmokers.(b)The population is all adolescents aged18–21. The sample consisted of 20,21118-year-old Israeli military recruits.(c)Descriptive statistics:The average IQ ofthe smokers was 94, and the average IQof nonsmokers was 101.(d)The conclusion is that individuals with alower IQ are more likely to choose tosmoke.44.(a)The research objective is to determine ifthe application of duct tape is as effectiveas cryotherapy in the treatment ofcommon warts.(b)The population is all people with warts.The sample consisted of 51 patients withwarts.(c)Descriptive statistics:85% of patients ingroup 1 and 60% of patients in group 2had complete resolution of their warts.(d)The conclusion is that duct tape issignificantly more effective in treatingwarts than cryotherapy.45.(a)The research objective is to determine theproportion of adult Americans whobelieve the federal government wastes51 cents or more of every dollar.(b)The population is all adult Americansaged 18 years or older.(c)The sample is the 1017 American adultsaged 18 years or older that weresurveyed.(d)Descriptive statistics:Of the 1017individuals surveyed, 35% indicated that51 cents or more is wasted.(e)From this study, one can infer that manyAmericans believe the federalgovernment wastes much of the moneycollected in taxes.

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Section 1.1:Introduction to the Practice of Statistics346.(a)The research objective is to determinewhat proportion of adults, aged 18 andover, believe it would be a bad idea toinvest $1000 in the stock market.(b)The population is all adults aged 18 andover living in the United States.(c)The sample is the 1018 adults aged 18 andover living in the United States whocompleted the survey.(d)Descriptive statistics:Of the 1016 adultssurveyed, 46% believe it would be a badidea to invest $1000 in the stock market.(e)The conclusion is that a little fewer thanhalf of the adults in the United Statesbelieve investing $1000 in the stockmarket is a bad idea.47.(a)State is aqualitativevariable because it isan individual categorization.(b)F scale is aqualitativevariable becauseeach tornado is rated according to acategory.(c)Fatalities is aquantitativevariablebecause it is a numerical measure. It is adiscretevariable because it is countable.(d)Length is aquantitativevariable becauseit is a numerical measure. It is acontinuousvariable because it resultsfrom measurement.48.(a)State is a variable measured at thenominallevel because values of thevariable name, label, or categorize. Inaddition, the naming scheme does notallow for the values of the variable to bearranged in a ranked or specific order.(b)F scale is a variable measured at theordinallevel because the naming schemeallows for the values of the variable to bearranged in a ranked or specific order.(c)Fatalities is a variable measured at theratiolevel because the ratio of two valuesmakes sense and a value of zero hasmeaning.(d)Length is a variable measured at the ratiolevel because the ratio of two valuesmakes sense and a value of zero hasmeaning.49.Jersey numberis nominal (the numbersgenerally indicate a type of position played).However, if the researcher feels that lowercaliber players received higher numbers, thenjersey numberwould be ordinal since playerscould be ranked by their number.50.(a)Nominal; the ticket number is categorizedas a winner or a loser.(b)Ordinal; the ticket number gives anindication as to the order of arrival ofguests.(c)Ratio; the implication is that the ticketnumber gives an indication of the numberof people attending the party.51.(a)The research question is to determine ifthe season of birth affects mood later inlife.(b)The sample consisted of the 400 peoplethe researchers studied.(c)The season in which you were born(winter, spring, summer, or fall) is aqualitative variable.(d)According to the article, individuals bornin the summer are characterized by rapid,frequent swings between sad and cheerfulmoods, while those born in the winter areless likely to be irritable.(e)The conclusion was that the season atbirth plays a role in one’s temperament.52.The population is the group to be studied asdefined by the research objective. A sample isany subset of the population.53.Quantitative variables are numerical measuressuch that meaningful arithmetic operations canbe performed on the values of the variable.Qualitative variables describe an attribute orcharacteristic of the individual that allowsresearchers to categorize the individual.The values of a discrete random variable resultfrom counting. The values of a continuousrandom variable result from a measurement.54.The four levels of measurement of a variableare nominal, ordinal, interval, and ratio.Examples: Nominal—brand of clothing;Ordinal—size of a car (small, mid-size, large);Interval—temperature (in degrees Celsius);Ratio—number of students in a class(Examples will vary.)

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4Chapter 1:Data Collection55.We say data vary, because when we draw arandom sample from a population, we do notknow which individuals will be included. Ifwe were to take another random sample, wewould have different individuals and thereforedifferent data. This variability affects theresults of a statistical analysis because theresults would differ if a study is repeated.56.The process of statistics is to (1) identify theresearch objective, which means to determinewhat should be studied and what we hope tolearn; (2) collect the data needed to answer theresearch question, which is typically done bytaking a random sample from a population; (3)describe the data, which is done by presentingdescriptive statistics; and (4) performinference in which the results are generalizedto a larger population.57.Age could be considered a discrete randomvariable. A random variable can be discrete byallowing, for example, only whole numbers tobe recorded.Section 1.21.The response variable is the variable ofinterest in a research study. An explanatoryvariable is a variable that affects (or explains)the value of the response variable. Inresearch, we want to see how changes in thevalue of the explanatory variable affect thevalue of the response variable.2.(a)III. A designed experiment is when aresearcher randomly assigns theindividuals in a study to groups,intentionally manipulates the value of anexplanatory variable, controls otherexplanatory variables at fixed values, andthen records the value of the responsevariable for each individual.(b)V. An observational study is when aresearcher measures the value of theresponse variable without attempting toinfluence the value of either the responseor explanatory variables. That is, theresearcher observes the behavior ofindividuals in the study and records thevalues of the explanatory and responsevariables.(c)IV. A lurking variable is an explanatoryvariable that was not considered in astudy, but that affects the value of theresponse variable in the study. In addition,this variable is typically related to otherexplanatory variables in the study.(d)I. Confounding occurs when the effects oftwo or more explanatory variables are notseparated. Therefore, any relation thatmay exist between an explanatoryvariable and the response variable may bedue to some other variable not accountedfor in the study.(e)II. A confounding variable is anexplanatory variable that was consideredin a study whose effect cannot bedistinguished from a second explanatoryvariable in the study.3.(a)II. A cohort study follows a group ofindividuals over a long period of time.Characteristics of the individuals arerecorded and some individuals will beexposed to certain factors (notintentionally) and others will not. Becausethe data are collected over time, cohortstudies are prospective.(b)III. A cross-sectional study collectsinformation about individuals at a specificpoint in time, or over a short period oftime.(c)I. A case-control study is retrospective,meaning it requires the researcher to lookat existing records, or the subject to recallinformation from the past. Individualswho have certain characteristics arematched with those who don’t.4.An observational study uses data obtained bystudying individuals in a sample withouttrying to manipulate or influence thevariable(s) of interest. In a designedexperiment, a treatment is applied to theindividuals in a sample in order to isolate theeffects of the treatment on a response variable.Only an experiment can establish causationbetween an explanatory variable and aresponse variable. Observational studies canindicate a relationship, but cannot establishcausation.5.The choice between an observational studyand an experiment depends on thecircumstances involved. Sometimes there areethical reasons why an experiment cannot beconducted. Other times the researcher mayconduct an observational study first to validatea belief prior to investing a large amount oftime and money into a designed experiment. Adesigned experiment is preferred if ethics,time, and money are not an issue.

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Section 1.2:Observational Studies vs. Designed Experiments56.A cohort study identifies the individuals toparticipate and then follows them over aperiod of time. During this period, informationabout the individuals is gathered, but there isno attempt to influence the individuals. Cohortstudies are superior to case-control studiesbecause cohort studies do not require recall toobtain the data.7.There is a perceived benefit to obtaining a flushot, so there are ethical issues in intentionallydenying certain seniors access to thetreatment.8.A retrospective study looks at data from thepast either through recall or existing records.A prospective study gathers data over time byfollowing the individuals in the study andrecording data as they occur.9.This is an observational study because theresearchers merely observed existing data.There was no attempt by the researchers tomanipulate or influence the variable(s) ofinterest.10.This is an experiment because the researchersintentionally changed the value of theexplanatory variable (medication dose) toobserve a potential effect on the responsevariable (cancer growth).11.This is an experiment because the explanatoryvariable (teaching method) was intentionallyvaried to see how it affected the responsevariable (score on proficiency test).12.This is an observational study because noattempt was made to influence the variable ofinterest. Voting choices were merelyobserved.13.This is an observational study because thesurvey only observed preference of Coke orPepsi. No attempt was made to manipulate orinfluence the variable of interest.14.This is an experiment because the researcherintentionally imposed treatments onindividuals in a controlled setting.15.This is an experiment because the explanatoryvariable (carpal tunnel treatment regimen) wasintentionally manipulated in order to observepotential effects on the response variable(level of pain).16.This is an observational study because theconservation agents merely observed the fishto determine which were carrying parasites.No attempt was made to manipulate orinfluence any variable of interest.17.(a)This is a cohort study because theresearchers observed a group of peopleover a period of time.(b)The response variable is whether theindividual has heart disease or not. Theexplanatory variable is whether theindividual is happy or not.(c)There may be confounding due to lurkingvariables. For example, happy peoplemay be more likely to exercise, whichcould affect whether they will have heartdisease or not.18.(a)This is a cross-sectional study becausethe researchers collected informationabout the individuals at a specific point intime.(b)The response variable is whether thewoman has nonmelanoma skin cancer ornot. The explanatory variable is the dailyamount of caffeinated coffee consumed.(c)It was necessary to account for thesevariables to avoid confounding with othervariables.19.(a)This is an observational study because theresearchers simply administered aquestionnaire to obtain their data. Noattempt was made to manipulate orinfluence the variable(s) of interest.This is a cross-sectional study becausethe researchers are observing participantsat a single point in time.(b)The response variable is body massindex. The explanatory variable iswhether a TV is in the bedroom or not.(c)Answers will vary. Some lurkingvariables might be the amount of exerciseper week and eating habits. Both of thesevariables can affect the body mass indexof an individual.(d)The researchers attempted to avoidconfounding due to other variables bytaking into account such variables as“socioeconomic status.”(e)No. Since this was an observationalstudy, we can only say that a television inthe bedroom is associated with a higherbody mass index.

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6Chapter 1:Data Collection20.(a)This is an observational study because theresearchers merely observed theindividuals included in the study. Noattempt was made to manipulate orinfluence any variable of interest.This is a cohort study because theresearchers identified the individuals tobe included in the study, then followedthem for a period of time (7 years).(b)The response variable is weight gain. Theexplanatory variable is whether theindividual is married/cohabitating or not.(c)Answers will vary. Some potentiallurking variables are eating habits,exercise routine, and whether theindividual has children.(d)No. Since this is an observational study,we can only say that being married orcohabitating is associated with weightgain.21.(a)This is a cross-sectional study becauseinformation was collected at a specificpoint in time (or over a very short periodof time).(b)The explanatory variable is deliveryscenario (caseload midwifery, standardhospital care, or private obstetric care).(c)The two response variables are (1) cost ofdelivery, which is quantitative, and (2)type of delivery (vaginal or not), which isqualitative.22.(a)The explanatory variable is web pagedesign; qualitative(b)The response variables are time on siteand amount spent. Both are qualitative.(c)Answers will vary. A confoundingvariable might be location. Anydifferences in spending may be due tolocation rather than to web page design.23.Answers will vary. This is a prospective,cohort observational study. The responsevariable is whether the worker had cancer ornot, and the explanatory variable is the amountof electromagnetic field exposure. Somepossible lurking variables include eatinghabits, exercise habits, and other health-relatedvariables such as smoking habits. Genetics(family history) could also be a lurkingvariable. This was an observational study, andnot an experiment, so the study only concludesthat high electromagnetic field exposure isassociated with higher cancer rates.The author reminds us that this is anobservational study, so there is no directcontrol over the variables that may affectcancer rates. He also points out that while weshould not simply dismiss such reports, weshould consider the results in conjunction withresults from future studies. The authorconcludes by mentioning known ways (basedon extensive study) of reducing cancer risksthat can currently be done in our lives.24.(a)This is a cohort study because a group ofindividuals was identified to participatein the study, and then they were observedover a period of time.(b)Because there is a link establishedbetween obesity and cell phone use, and alink between obesity and negative healthoutcomes, if it is determined that cell-phone users are experiencing higherincidence rates of negative healthoutcomes, it cannot be established thatthe factor leading to the negative healthoutcome is due to the cell phone—it maybe due to the lurking variable obesity.25.Because individuals in the early 1900s werepressured to become right-handed, we wouldsee a lower proportion of left-handers who areolder in the study. This would make it seem asthough left-handers die younger because theolder individuals in the study are primarilyright-handed.26.(a)The research objective is to determinewhether lung cancer is associated withexposure to tobacco smoke within thehousehold.(b)This is a case-controlled study becausethere is a group of individuals with acertain characteristic (lung cancer butnever smoked) being compared to asimilar group without the characteristic(no lung cancer and never smoked). Thestudy is retrospective because lifetimeresidential histories were compiled andanalyzed.(c)The response variable is whether theindividual has lung cancer or not. This isa qualitative variable.

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Section 1.3:Simple Random Sampling7(d)The explanatory variable is the number of“smoker years.” This is a quantitativevariable.(e)Answers will vary. Some possible lurkingvariables are household income, exerciseroutine, and exposure to tobacco smokeoutside the home.(f)The conclusion of the study is thatapproximately 17% of lung cancer casesamong nonsmokers can be attributed tohigh levels of exposure to tobacco smokeduring childhood and adolescence. No,we cannot say that exposure to householdtobacco smoke causes lung cancer sincethis is only an observational study. Wecan, however, conclude that lung canceris associated with exposure to tobaccosmoke in the home.(g)An experiment involving human subjectsis not possible for ethical reasons.Researchers would be able to conduct anexperiment using laboratory animals,such as rats.27.Web scraping can be used to extract data fromtables on web pages and then upload the datato a file. Web scraping can also be used tocreate a data set of words from an onlinearticle (that is, fetching unstructuredinformation and transforming it into astructured format through something calledparsing and reformatting processes). Inaddition, web scraping can be used todynamically call information from websiteswith links.28.Answers will vary. Discussions may includethe responsibility of host sites to protectprivate information; the ethics behind usinginformation collected from a site to harm acompetitor; the ethics behind putting stress ona host’s servers so that the website slowsdown; the role of social media to scrape itssite for “fake news.”Section 1.31.The frame is a list of all the individuals in thepopulation.2.Simple random sampling occurs when everypossible sample of sizenhas an equally likelychance of occurring.3.Sampling without replacement means that noindividual may be selected more than once asa member of the sample.4.Random sampling is a technique that useschance to select individuals from a populationto be in a sample. It is used because itmaximizes the likelihood that the individualsin the sample are representative of theindividuals in the population. In conveniencesampling, the individuals in the sample areselected in the quickest and easiest waypossible (e.g. the first 20 people to enter astore). Convenience samples likely do notrepresent the population of interest becausechance was not used to select the individuals.5.Answers will vary. We will use one-digitlabels and assign the labels across each row(i.e.Pride and Prejudice– 0,The Sun AlsoRises– 1, and so on). In Table I of AppendixA, starting at row 5, column 11, andproceeding downward, we obtain thefollowing labels: 8, 4, 3In this case, the 3 books in the sample wouldbeAs I Lay Dying,A Tale of Two Cities, andCrime and Punishment. Different labelingorder, different starting points in Table I inAppendix A, or use of technology will likelyyield different samples.6.Answers will vary. We will use one-digitlabels and assign the labels across each row(i.e.Mady– 0,Breanne– 1, and so on). InTable I of Appendix A, starting at row 11,column 6, and then proceeding downward, weobtain the following labels: 1, 5In this case, the two captains would beBreanne and Payton. Different labeling order,different starting points in Table I inAppendix A, or use of technology will likelyyield different results.7.(a){616, 630}, {616, 631}, {616, 632},{616, 645}, {616, 649}, {616, 650},{630, 631}, {630, 632}, {630, 645},{630, 649}, {630, 650}, {631, 632},{631, 645}, {631, 649}, {631, 650},{632, 645}, {632, 649}, {632, 650},{645, 649}, {645, 650}, {649, 650}(b)There is a 1 in 21 chance that the pair ofcourses will be EPR 630 and EPR 645.8.(a){1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6},{1, 7}, {2, 3}, {2, 4}, {2, 5}, {2, 6},{2, 7}, {3, 4}, {3, 5}, {3, 6}, {3, 7},{4, 5}, {4, 6}, {4, 7}, {5, 6}, {5, 7},{6, 7}(b)There is a 1 in 21 chance that the pairThe United NationsandAmnestyInternationalwill be selected.

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8Chapter 1:Data Collection9.(a)Starting at row 5, column 22, using two-digit numbers, and proceedingdownward, we obtain the followingvalues: 83, 94, 67, 84, 38, 22, 96, 24, 36,36, 58, 34,.... We must disregard 94 and96 because there are only 87 facultymembers in the population. We must alsodisregard the second 36 because we aresampling without replacement. Thus, the9 faculty members included in the sampleare those numbered 83, 67, 84, 38, 22, 24,36, 58, and 34.(b)Answers will vary depending on the typeof technology used. If using a TI-84 Plus,the sample will be: 4, 20, 52, 5, 24, 87,67, 86, and 39.Note: We must disregard the second 20because we are sampling withoutreplacement.10.(a)Starting at row 11, column 32, using four-digit numbers, and proceedingdownward, we obtain the followingvalues: 2869, 5518, 6635, 2182, 8906,0603, 2654, 2686, 0135, 7783, 4080,6621, 3774, 7887, 0826, 0916, 3188,0876, 5418, 0037, 3130, 2882, 0662,….We must disregard 8906, 7783, and 7887because there are only 7656 students inthe population.Thus, the 20 students included in thesample are those numbered 2869, 5518,6635, 2182, 0603, 2654, 2686, 0135,4080, 6621, 3774, 0826, 0916, 3188,0876, 5418, 0037, 3130, 2882, and 0662.(b)Answers may vary depending on the typeof technology used. If using a TI-84 Plus,the sample will be: 6658, 4118, 9, 4828,3905, 454, 2825, 2381, 495, 4445, 4455,5759, 5397, 7066, 3404, 6667, 5074,3777, 3206, 5216.11.(a)Answers will vary depending on thetechnology used (including a table ofrandom digits). Using a TI-84 Plusgraphing calculator with a seed of 17 andthe labels provided, our sample would beNorth Dakota, Nevada, Tennessee,Wisconsin, Minnesota, Maine, NewHampshire, Florida, Missouri, andMississippi.(b)Repeating part (a) with a seed of 18, oursample would be Michigan,Massachusetts, Arizona, Minnesota,Maine, Nebraska, Georgia, Iowa, RhodeIsland, and Indiana.12.(a)Answers will vary depending on thetechnology used (including a table ofrandom digits). Using a TI-84 Plusgraphing calculator with a seed of 98 andthe labels provided, our sample would beJefferson, Reagan, Madison, Trump,Pierce, Buchanan, Carter, G. W. Bush.(b)Repeating part (a) with a seed of 99, oursample would be Nixon, Eisenhower,Pierce, Arthur, Trump, Hayes, Clinton,T. Roosevelt.

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Solution Manual for Fundamentals of Statistics, 6th Edition - Page 14 preview image

Section 1.4:Other Effective Sampling Methods913.(a)The list provided by the administrationserves as the frame. Number each studentin the list of registered students, from 1 to19,935. Generate 25 random numbers,without repetition, between 1 and 19,935using a random number generator ortable. Select the 25 students with thesenumbers.(b)Answers will vary.14.(a)The list provided by the mayor serves asthe frame. Number each resident in thelist supplied by the mayor, from 1 to5832. Generate 20 random numbers,without repetition, between 1 and 5832using a random number generator ortable. Select the 20 residents with thesenumbers.(b)Answers will vary.15.Answers will vary. Members should benumbered 1–32, though other numberingschemes are possible (e.g. 0–31). Using atable of random digits or a random-numbergenerator, four different numbers (labels)should be selected. The names correspondingto these numbers form the sample.16.Answers will vary. Employees should benumbered 1–29, though other numberingschemes are possible (e.g. 0–28). Using atable of random digits or a random-numbergenerator, four different numbers (labels)should be selected. The names correspondingto these numbers form the sample.17.Answers will vary.Section 1.41.Stratified random sampling may beappropriate if the population of interest can bedivided into groups (or strata) that arehomogeneous and nonoverlapping.2.Systematic sampling does not require a frame.3.Convenience samples are typically selected ina nonrandom manner. This means the resultsare not likely to represent the population.Convenience samples may also be self-selected, which will frequently result in smallportions of the population beingoverrepresented.4.Cluster sample5.Stratified sample6.False. In a systematic random sample, everykth individual is selected from the population.7.False. In many cases, other samplingtechniques may provide equivalent or moreinformation about the population with less“cost” than simple random sampling.8.True. When the clusters are heterogeneous, theheterogeneity of each cluster likely resemblesthe heterogeneity of the population. In suchcases, fewer clusters with more individualsfrom each cluster are preferred.9.True. Because the individuals in aconvenience sample are not selected usingchance, it is likely that the sample is notrepresentative of the population.10.False. With stratified samples, the number ofindividuals sampled from each strata shouldbe proportional to the size of the strata in thepopulation.11.Systematic sampling. The quality-controlmanager is sampling every 8thchip, startingwith the 3rdchip.12.Cluster sampling. The commission tests allmembers of the selected teams (clusters).13.Cluster sampling. The airline surveys allpassengers on selected flights (clusters).14.Stratified sampling. The congresswomansamples some individuals from each of threedifferent income brackets (strata).15.Simple random sampling. Each known user ofthe product has the same chance of beingincluded in the sample.16.Convenience sampling. The radio station isrelying on voluntary response to obtain thesample data.17.Cluster sampling. The farmer samples all treeswithin the selected subsections (clusters).18.Stratified sampling. The school official takes asample of students from each of the fiveclasses (strata).19.Convenience sampling. The research firm isrelying on voluntary response to obtain thesample data.20.Systematic sampling. The presider is samplingevery 5thperson attending the lecture, startingwith the 3rdperson.

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Solution Manual for Fundamentals of Statistics, 6th Edition - Page 15 preview image

110Chapte21.Stratifiedmeasureintervals22.Simple rhas the ssurvey.23.The numselected6625+216, 241441, 46624.Since thbut lessthree-digStartingAppendi10 cluste377, 304Note thathe tablethese laboccurrenthe same25.Answersnumbersimple rthe Repurandomdifferentseed forFor examcalculatoand 40 fselected14, 4 forthe indivwould cand Eng26.Answersnumbersimple rthe emprandomdifferentseed forer 1:Data Cd sampling. Shements during es (strata).random samplisame chance ofmbers corresponare16,162+91=,9125+=1, 266, 291, 316, 491.e number of clthan 1000, wegit label betweat row 8, columix A, and proceers selected are4, 626, 392, 31at we discard 8e because we hbels. We also dnce of 377 becae cluster twice.s will vary. Tothe Democratsrandom sampleublicans 1 to 1sample of sizet starting pointeach stratum.mple, using a Tor with a seedfor the Republiwould be 6, 9r the Republicaviduals down eonsist of Haydgler.s will vary. Tothe managersrandom sampleloyees 1 to 21sample of sizet starting pointeach stratum.ollectionhawn takes a saeach of the foung. Each clubf being selectending to the 202541=,412+116=, 141, 166, 341, 366, 39lusters is moreassign each cleen 001 and 79mn 38 in Tableeeding downwe numbered 765, 084, 565, an22 and 955 inhave no clustersdiscard the secoause we canno.obtain the sams 1 to 16 and obe of size 2. The6 and obtain ae 2. Be sure to ut in Table I or aTI-84 Plus grapof 38 for the Dicans, the numbfor the Democans. If we had neach column, thdra, Motola, Thobtain the sam1 to 8 and obtae of size 2. Theand obtain a sie 4. Be sure to ut in Table I or aCopyright © 2ample ofur timememberd for the0 clients2566=,6, 191,91, 416,than 100,luster a5.e I ofward, the63, 185,nd 508.readings withondt selectmple,btain aen numbersimpleuse aa differentphingDemocratsberscrats andnumberedhe samplehompson,mple,ain aen numberimpleuse aa different2022 Pearson EFocalansel20nutheW27.(a)(b)28.(a)(b)29.SimStrClu30.NoThsamEducation, Inc.or example, usilculator with and 20 for the emlected would b0, 3, 11, 9 for thumbered the inde sample wouldWeber, Bryant, H)450250Nn==)Randomly s90. Supposeindividuals t15th, 105th,the 4425th e)94503130Nn=7269k=.)Randomly s7269. Suppo2000. Thennumbered 2up to the indmple RandomNumber thea table of ranumber genstudents to sratified SampleSince class swant to randstudents fromthe sample.uster Sample:Since classemakeup, weselect12832=students fromo. The clustershis would be compling..ing a TI-84 Pluaseed of 18 formployees, thenbe 4, 1 for themhe employees.dividuals downd consist of LiHall, and Gow90.0490=®;select a numberethat we selectto be surveyed,195th, 285th,employee on th57269.5=®select a numberose that we ranwe will survey000, 9269, 16,dividual numbeSample:estudents fromandom digits ornerator to randosurvey.e:sizes are similadomly select13meach class toes are similar inewould want to4=classes andmthose classewere not randoonsidered convus graphingrthe managersnumbersmanagers andIf we hadneach columnndsey, Carlisle.;Thus,90k=rbetween 1 ant15. Then thedwill be theand so on upthe company lis7269; Thus,rbetween 1 anndomly selectythe individua,538, and so onered 939,701.m1 to 1280. Usra random-omly select 128ar, we would28432 =obe includedinsize andorandomlydinclude all thes in the sampleomly selected.venience,e,.ndtost.ndalsne8inhee.

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Solution Manual for Fundamentals of Statistics, 6th Edition - Page 16 preview image

Section 1.5:Bias in Sampling1131.Answers will vary. One design would be astratified random sample, with two stratabeing commuters and noncommuters, as thesetwo groups each might be fairly homogeneousin their reactions to the proposal.32.Answers will vary. One design would be acluster sample, with classes as the clusters.Randomly select clusters and then survey allthe students in the selected classes. However,care would need to be taken to make sure thatno one was polled twice. Since this wouldnegate some of the ease of cluster sampling, asimple random sample might be the moresuitable design.33.Answers will vary. One design would be acluster sample, with the clusters being cityblocks. Randomly select city blocks andsurvey every household in the selected blocks.34.Answers will vary. One appropriate designwould be a systematic sample, after doing arandom start, clocking the speed of everytenth car, for example.35.Answers will vary. Since the company alreadyhas a list (frame) of 6600 individuals withhigh cholesterol, a simple random samplewould be an appropriate design.36.Answers will vary. Since a list of all thehouseholds in the population exists, a simplerandom sample is possible. Number thehouseholds from 1 toN, then use a table ofrandom digits or a random-number generatorto select the sample.37.(a)For a political poll, a good frame wouldbe all registered voters who have voted inthe past few elections since they are morelikely to vote in upcoming elections.(b)Because each individual from the framehas the same chance of being selected,there is a possibility that one group maybe over- or underrepresented.(c)By using a stratified sample, the strategistcan obtain a simple random samplewithin each strata (political party) so thatthe number of individuals in the sample isproportionate to the number ofindividuals in the population.38.Random sampling means that the individualschosen to be in the sample are selected bychance. Random sampling minimizes thechance that one part of the population is over-or underrepresented in the sample. However,it cannot guarantee that the sample willaccurately represent the population.39.Answers will vary.40.Answers will vary.Section 1.51.A closed question is one in which therespondent must choose from a list ofprescribed responses. An open question is onein which the respondent is free to choose hisor her own response. Closed questions areeasier to analyze, but limit the responses.Open questions allow respondents to stateexactly how they feel, but are harder toanalyze due to the variety of answers andpossible misinterpretation of answers.2.A certain segment of the population isunderrepresented if it is represented in thesample in a lower proportion than its size inthe population.3.(a)III. Bias occurs when the results of thesample are not representative of thepopulation.(b)I. Sampling bias occurs when thetechniques used to select individuals for asample favor one part of the populationover another.(c)IV. Nonresponse bias occurs when theindividuals selected to be in the samplewho do not respond to the survey havedifferent opinions from those who dorespond.(d)II. Response bias occurs when theanswers on a survey do not reflect the truefeelings of the respondent.4.Nonsampling error is the error that resultsfrom undercoverage, nonresponse bias,response bias, or data-entry errors. Essentially,it is the error that results from the process ofobtaining and recording data. Sampling erroris the error that results because a sample isbeing used to estimate information about apopulation. Any error that could also occur ina census is considered a nonsampling error.5.(a)Sampling bias. The survey suffers fromundercoverage because the first60 customers are likely notrepresentative of the entire customerpopulation.(b)Since a complete frame is not possible,systematic random sampling could beused to make the sample morerepresentative of the customer population.

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