Solution Manual for Fundamentals of Statistics, 5th Edition

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SOLUTIONSMANUALGEXPUBLISHINGSERVICESFUNDAMENTALS OFSTATISTICS:INFORMEDDECISIONSUSINGDATAFIFTHEDITIONMichael 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 .........................................................................................31.3Simple Random Sampling ..................................................................................................................................61.4Other Effective Sampling Methods.....................................................................................................................81.5Bias in Sampling ...............................................................................................................................................101.6The Design of Experiments ..............................................................................................................................13Chapter 1 Review Exercises ........................................................................................................................................19Chapter 1 Test..............................................................................................................................................................22Chapter 2Summarizing Data in Tables and Graphs2.1Organizing Qualitative Data .............................................................................................................................252.2Organizing Quantitative Data ...........................................................................................................................332.3Graphical Misrepresentations of Data...............................................................................................................47Chapter 2 Review Exercises ........................................................................................................................................49Chapter 2 Test..............................................................................................................................................................54Chapter 3Numerically Summarizing Data3.1Measures of Central Tendency .........................................................................................................................573.2Measures of Dispersion.....................................................................................................................................643.3Measures of Central Tendency and Dispersion from Grouped Data ................................................................803.4Measures of Position and Outliers ....................................................................................................................893.5The Five-Number Summary and Boxplots .......................................................................................................97Chapter 3 Review Exercises ......................................................................................................................................106Chapter 3 Test............................................................................................................................................................111Chapter 4Describing the Relation between Two Variables4.1Scatter Diagrams and Correlation ...................................................................................................................1164.2Least-Squares Regression ...............................................................................................................................1334.3The Coefficient of Determination ...................................................................................................................1444.4Contingency Tables and Association ..............................................................................................................148Chapter 4 Review Exercises ......................................................................................................................................155Chapter 4 Test............................................................................................................................................................160Chapter 5Probability5.1Probability Rules.............................................................................................................................................1645.2The Addition Rule and Complements.............................................................................................................1705.3Independence and the Multiplication Rule .....................................................................................................1775.4Conditional Probability and the General Multiplication Rule.........................................................................1815.5Counting Techniques ......................................................................................................................................1875.6Putting It Together: Which Method Do I Use? ...............................................................................................192Chapter 5 Review Exercises ......................................................................................................................................194Chapter 5 Test............................................................................................................................................................197

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Chapter 6Discrete Probability Distributions6.1Discrete Random Variables.............................................................................................................................2006.2The Binomial Probability Distribution............................................................................................................208Chapter 6 Review Exercises ......................................................................................................................................222Chapter 6 Test............................................................................................................................................................225Chapter 7The Normal Probability Distribution7.1Properties of the Normal Distribution .............................................................................................................2287.2Applications of the Normal Distribution.........................................................................................................2317.3Assessing Normality .......................................................................................................................................2507.4The Normal Approximation to the Binomial Probability Distribution ...........................................................253Chapter 7 Review Exercises ......................................................................................................................................257Chapter 7 Test............................................................................................................................................................262Chapter 8Sampling Distributions8.1Distribution of the Sample Mean ....................................................................................................................2668.2Distribution of the Sample Proportion ............................................................................................................278Chapter 8 Review Exercises ......................................................................................................................................284Chapter 8 Test............................................................................................................................................................287Chapter 9Estimating the Value of a Parameter9.1Estimating a Population Proportion ................................................................................................................2899.2Estimating a Population Mean ........................................................................................................................2959.3Putting It Together: Which Procedure Do I Use?............................................................................................305Chapter 9 Review Exercises ......................................................................................................................................310Chapter 9 Test............................................................................................................................................................314Chapter 10 Hypothesis Tests Regarding a Parameter10.1The Language of Hypothesis Testing..............................................................................................................31710.2Hypothesis Tests for a Population Proportion.................................................................................................32010.3Hypothesis Tests for a Population Mean.........................................................................................................32910.4Putting It Together: Which Method Do I Use? ...............................................................................................338Chapter 10 Review Exercises ....................................................................................................................................342Chapter 10 Test..........................................................................................................................................................346Chapter 11 Inferences on Two Samples11.1Inference about Two Population Proportions..................................................................................................34811.2Inference about Two Means: Dependent Samples ..........................................................................................36111.3Inference about Two Means: Independent Samples........................................................................................37111.4Putting It Together: Which Method Do I Use? ...............................................................................................385Chapter 11 Review Exercises (Online) ......................................................................................................................398Chapter 11 Test..........................................................................................................................................................404Chapter 12 Additional Inferential Techniques12.1Goodness-of-Fit Test.......................................................................................................................................41012.2Tests for Independence and the Homogeneity of Proportions.........................................................................42112.3Testing the Significance of the Least-Squares Regression Model ..................................................................43912.4Confidence and Prediction Intervals ...............................................................................................................445Chapter 12 Review Exercises ....................................................................................................................................451Chapter 12 Test..........................................................................................................................................................458

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Chapter 1Data CollectionSection 1.11.Statistics is the science of collecting,organizing, summarizing, and analyzinginformation in order to draw conclusions andanswer questions. In addition, statistics isabout providing a measure of confidence inany conclusions.2.The population is the group to be studied asdefined by the research objective. A sample isany subset of the population.3.Individual4.Descriptive; Inferential5.Statistic; Parameter6.Variables7.18% is a parameter because it describes apopulation (all of the governors).8.72% is a parameter because it describes apopulation (the entire class).9.32% is a statistic because it describes a sample(the high school students surveyed).10.9.6% is a statistic because it describes asample (the youths surveyed).11.0.366 is a parameter because it describes apopulation (all of Ty Cobb’s at-bats).12.43.92 hours is a parameter because it describesa population (all the men who have walked onthe moon).13.23% is a statistic because it describes a sample(the 6076 adults studied).14.44% is a statistic because it describes a sample(the 100 adults interviewed).15.Qualitative16.Quantitative17.Quantitative18.Qualitative19.Quantitative20.Quantitative21.Qualitative22.Qualitative23.Discrete24.Continuous25.Continuous26.Discrete27.Continuous28.Continuous29.Discrete30.Continuous31.Nominal32.Ordinal33.Ratio34.Interval35.Ordinal36.Nominal37.Ratio38.Interval39.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.40.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.41.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.42.The population consists of all householdswithin the United States. The sample consistsof the 50,000 households that are surveyed bythe U.S. Census Bureau.43.The population consists of all women 27 to44 years of age with hypertension. Thesample consists of the 7373 women 27 to 44years of age with hypertension who wereincluded in the study.44.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.

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2Chapter 1:Data Collection45.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.)46.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, RoadsterCoupe; 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.47.(a)The research objective is to determine ifadolescents aged 18–21 who smoke havea lower IQ than 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.48.(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.49.(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 31% to39% of Americans believe the federalgovernment wastes much of the moneycollected in taxes.50.(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 1018 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.51.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.

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Section 1.2:Observational Studies vs. Designed Experiments352.(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.53.(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.54.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.55.The values of a discrete random variable resultfrom counting. The values of a continuousrandom variable result from a measurement.56.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.)57.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.58.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.59.Age could be considered a discrete randomvariable. A random variable can be discreteby allowing, for example, only whole numbersto be 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. In research,we want to see how changes in the value ofthe explanatory variable affect the value of theresponse variable.2.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.3.Confounding exists in a study when the effectsof two or more explanatory variables are notseparated. So any relation that appears to existbetween a certain explanatory variable and theresponse variable may be due to some othervariable or variables not accounted for in thestudy. A lurking variable is a variable notaccounted for in a study, but one that affectsthe value of the response variable. Aconfounding variable is an explanatoryvariable that was considered in a study whoseeffect cannot be distinguished from a secondexplanatory variable in the study.

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4Chapter 1:Data Collection4.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.5.Cross-sectional studies collect information at aspecific point in time (or over a very shortperiod of time). Case-control studies areretrospective (they look back in time). Also,individuals that have a certain characteristic(such as cancer) in a case-control study arematched with those that do not have thecharacteristic. Case-control studies aretypically superior to cross-sectional studies.They are relatively inexpensive, provideindividual level data, and give longitudinalinformation not available in a cross-sectionalstudy.6.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.

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Section 1.2:Observational Studies vs. Designed Experiments519.(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.20.(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 isquantitative.22.(a)The explanatory variable is web pagedesign; qualitative(b)The response variables are time on siteand amount spent. Both are quantitative.(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)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.

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6Chapter 1:Data Collection(c)The response variable is whether theindividual has lung cancer or not. This isa qualitative variable.(d)The explanatory variable is the number of“smoker years.” This is a quantitativevariable.(e)Answers will vary. Some possiblelurking variables are household income,exercise routine, and exposure to tobaccosmoke outside 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.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.9.(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 mustalso disregard the second 36 because weare sampling without replacement. Thus,the 9 faculty members included in thesample are those numbered 83, 67, 84,38, 22, 24, 36, 58, and 34.

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Section 1.3:Simple Random Sampling7(b)Answers will vary depending on the typeof technology used. If using a TI-84Plus, 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-84Plus, 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, 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, Carter, Madison, Obama,Pierce, Buchanan, Ford, Clinton.(b)Repeating part (a) with a seed of 99, oursample would be L. B. Johnson, Truman,Pierce, Garfield, Obama, Grant, GeorgeH. Bush, T. Roosevelt.13.(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.

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8Chapter 1:Data Collection16.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.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,the heterogeneity of each cluster likelyresembles the heterogeneity of the population.In such cases, fewer clusters with moreindividuals from 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 alltrees within 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.21.Stratified sampling. Shawn takes a sample ofmeasurements during each of the four timeintervals (strata).22.Simple random sampling. Each club memberhas the same chance of being selected for thesurvey.23.The numbers corresponding to the 20 clientsselected are16,162541+=,412566+=,662591+=,9125116+=, 141, 166, 191,216, 241, 266, 291, 316, 341, 366, 391, 416,441, 466, 491.24.Since the number of clusters is more than 100,but less than 1000, we assign each cluster athree-digit label between 001 and 795.Starting at row 8, column 38 in Table I ofAppendix A, and proceeding downward, the10 clusters selected are numbered 763, 185,377, 304, 626, 392, 315, 084, 565, and 508.Note that we discard 822 and 955 in readingthe table because we have no clusters withthese labels. We also discard the secondoccurrence of 377 because we cannot selectthe same cluster twice.

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Section 1.4:Other Effective Sampling Methods925.Answers will vary. To obtain the sample,number the Democrats 1 to 16 and obtain asimple random sample of size 2. Then numberthe Republicans 1 to 16 and obtain a simplerandom sample of size 2. Be sure to use adifferent starting point in Table I or a differentseed for each stratum.For example, using a TI-84 Plus graphingcalculator with a seed of 38 for the Democratsand 40 for the Republicans, the numbersselected would be 6, 9 for the Democrats and14, 4 for the Republicans. If we had numberedthe individuals down each column, the samplewould consist of Haydra, Motola, Thompson,and Engler.26.Answers will vary. To obtain the sample,number the managers 1 to 8 and obtain asimple random sample of size 2. Then numberthe employees 1 to 21 and obtain a simplerandom sample of size 4. Be sure to use adifferent starting point in Table I or a differentseed for each stratum.For example, using a TI-84 Plus graphingcalculator with a seed of 18 for the managersand 20 for the employees, the numbersselected would be 4, 1 for the managers and20, 3, 11, 9 for the employees. If we hadnumbered the individuals down each column,the sample would consist of Lindsey, Carlisle,Weber, Bryant, Hall, and Gow.27.(a)450290.049050Nn==→; Thus,90k=.(b)Randomly select a number between 1 and90. Suppose that we select 15. Then theindividuals to be surveyed will be the15th, 105th, 195th, 285th, and so on up tothe 4425th employee on the company list.28.(a)9450357269.57269130Nn==→; Thus,7269k=.(b)Randomly select a number between 1 and7269. Suppose that we randomly select2000. Then we will survey theindividuals numbered 2000, 9269,16,538, and so on up to the individualnumbered 939,701.29.Simple Random Sample:Number the students from 1 to 1280. Usea table of random digits or a random-number generator to randomly select 128students to survey.Stratified Sample:Since class sizes are similar, we wouldwant to randomly select 128432=students from each class to be included inthe sample.Cluster Sample:Since classes are similar in size andmakeup, we would want to randomlyselect 128432=classes and include all thestudents from those classes in the sample.30.No. The clusters were not randomly selected.This would be considered conveniencesampling.31.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.

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Solution Manual for Fundamentals of Statistics, 5th Edition - Page 14 preview image

10Chapter 1:Data Collection35.Answers will vary. Since the companyalready has a list (frame) of 6600 individualswith high 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.Bias means that the results of the sample arenot representative of the population. There arethree types of bias: sampling bias, responsebias, and nonresponse bias. Sampling bias isdue to the use of a sample to describe apopulation. This includes bias due toconvenience sampling. Response biasinvolves intentional or unintentionalmisinformation. This would include lying to asurveyor or entering responses incorrectly.Nonresponse bias results when individualschoose not to respond to questions or areunable to be reached. A census can sufferfrom response bias and nonresponse bias, butwould not suffer from sampling bias.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.6.(a)Sampling bias. The survey suffers fromundercoverage because only homes in thesouthwest corner have a chance to beinterviewed. These homes may havedifferent demographics than those inother parts of the village.(b)Assuming that households within anygiven neighborhood have similarhousehold incomes, stratified samplingmight be appropriate, with neighborhoodsas the strata.7.(a)Response bias. The survey suffers fromresponse bias because the question ispoorly worded.

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Section 1.5:Bias in Sampling11(b)The survey should inform the respondentof the current penalty for selling a gunillegally and the question should beworded as “Do you approve ordisapprove of harsher penalties forindividuals who sell guns illegally?” Theorder of “approve” and “disapprove”should be switched from one individualto the next.8.(a)Response bias. The survey suffers fromresponse bias because the wording of thequestion is ambiguous.(b)The question might be worded morespecifically as “How many hours pernight do you sleep, on average?”9.(a)Nonresponse bias. Assuming the surveyis written in English, non-Englishspeaking homes will be unable to read thesurvey. This is likely the reason for thevery low response rate.(b)The survey can be improved by usingface-to-face or phone interviews,particularly if the interviewers are multi-lingual.10.(a)Nonresponse bias(b)The survey can be improved by usingface-to-face or phone interviews, orpossibly through the use of incentives.11.(a)The survey suffers from sampling biasdue to undercoverage and interviewererror. The readers of the magazine maynot be representative of all Australianwomen, and advertisements and imagesin the magazine could affect the women’sview of themselves.(b)A well-designed sampling plan not in amagazine, such as a cluster sample, couldmake the sample more representative ofthe population.12.(a)The survey suffers from sampling biasdue to a bad sampling plan (conveniencesampling) and possible response bias dueto misreported weights on driver’slicenses.(b)The teacher could use cluster sampling orstratified sampling using classesthroughout the day. Each student shouldbe weighed to get a current and accurateweight measurement.13.(a)Response bias due to a poorly wordedquestion(b)The question should be reworded in amore neutral manner. One possiblephrasing might be “Do you believe that amarriage can be maintained after anextramarital relation?”14.(a)Sampling bias. The frame is notnecessarily representative of all collegeprofessors.(b)To remedy this problem, the publishercould use cluster sampling and obtain alist of faculty from the human resourcesdepartments at selected colleges.15.(a)Response bias. Students are unlikely togive honest answers if their teacher isadministering the survey.(b)An impartial party should administer thesurvey in order to increase the rate oftruthful responses.16.(a)Response bias. Residents are unlikely togive honest answers to uniformed policeofficers if their answer would be seen asnegative by the police.(b)An impartial party should administer thesurvey in order to increase the rate oftruthful responses.17.No. The survey still suffers from samplingbias due to undercoverage, nonresponse bias,and potentially response bias.18.The General Social Survey uses randomsampling to obtain individuals who take thesurvey, so the results of their survey are morelikely to be representative of the population.However, it may suffer from response biassince the survey is conducted by personalinterview rather than anonymously on theInternet. The online survey, while potentiallyobtaining more honest answers, is basicallyself-selected so may not be representative ofthe population, particularly if mostrespondents are clients of the family andwellness center seeking help with health orrelationship problems.19.It is very likely that the order of these twoquestions will affect the survey results. Toalleviate the response bias, either question Bcould be asked first, or the order of the twoquestions could be rotated randomly.

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12Chapter 1:Data Collection20.It is very likely that the order of these twoquestions will affect the survey results. Toalleviate the response bias, the order of thetwo questions could be rotated randomly.Prohibit is a strong word. People generally donot like to be prohibited from doing things. Ifthe word must be used, it should be offset bythe word “allow.” The use of the words“prohibit” and “allow” should be rotatedwithin the question.21.The company is using a reward in the form ofthe $5.00 payment and an incentive by tellingthe reader that his or her input will make adifference.22.The two choices need to be rotated so that anyresponse bias due to the ordering of thequestions is minimized.23.For random digit dialing, the frame is anyonewith a phone (whose number is not on a do-not-call registry). Even those with unlistednumbers can still be reached through thismethod.Any household without a phone, householdson the do-not-call registry, and homelessindividuals are excluded. This could result insampling bias due to undercoverage if theexcluded individuals differ in some way thanthose included in the frame.24.Answers will vary. The use of caller ID haslikely increased nonresponse bias of phonesurveys since individuals may not answer callsfrom numbers they do not recognize. Ifindividuals with caller ID differ in some wayfrom individuals without caller ID, then phonesurveys could also suffer from sampling biasdue to undercoverage.25.It is extremely likely, particularly ifhouseholds on the do-not-call registry have atrait that is not part of those households thatare not on the registry.26.There is a higher chance that an individual atleast 70 years of age will be at home when aninterviewer makes contact.27.Some nonsampling errors presented in thearticle as leading to incorrect exit polls werepoorly trained interviewers, interviewer bias,and over representation of female voters.28.– 32.Answers will vary.33.TheLiterary Digestmade an incorrectprediction due to sampling bias (an incorrectframe led to undercoverage) and nonresponsebias (due to the low response rate).34.Answers will vary. (Gallup incorrectlypredicted the outcome of the 1948 electionbecause he quit polling weeks before theelection and missed a large number ofchanging opinions.)35.(a)Answers will vary. Stratified samplingby political affiliation (Democrat,Republican, etc.) could be used to ensurethat all affiliations are represented. Onequestion that could be asked is whether ornot the person plans to vote in the nextelection. This would help determinewhich registered voters are likely to vote.(b)Answers will vary. Possible explanationsare that presidential election cycles getmore news coverage or perhaps peopleare more interested in voting when theycan vote for a president as well as asenator. During non-presidential cycles itis very informative to poll likelyregistered voters.(c)Answers will vary. A higher percentageof Democrats in polls versus turnout willlead to overstating the predictedDemocrat percentage of Democraticvotes.36.It is difficult for a frame to be completelyaccurate since populations tend to change overtime and there can be a delay in identifyingindividuals who have joined or left thepopulation.37.Nonresponse can be addressed by conductingcallbacks or offering rewards.38.Trained, skillful interviewers can elicitresponses from individuals and help them givetruthful responses.39.Conducting a presurvey with open questionsallows the researchers to use the most popularanswers as choices on closed-questionsurveys.40.Answers will vary. Phone surveys conductedin the evening may result in reaching morepotential respondents; however some of theseindividuals could be upset by the intrusion.

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