Fundamentals of Statistics

605 Pages·2006·239.782 MB·English

by  Michael Sullivan

1
Getting the
Information
PART
You Need
CHAPTER1
DataCollection
Statisticsisaprocess—aseriesofstepsthatleadtoagoal. The first step in the process is to determine the re-
Thistextisdividedintofourpartstohelpthereadersee searchobjectiveorquestiontobeanswered.Then,infor-
theprocessofstatistics. mation is obtained to answer the questions stated in the
researchobjective.
1
1
Data Collection
CHAPTER
Outline
1.1 IntroductiontothePracticeofStatistics
1.2 ObservationalStudies,Experiments,andSimple
RandomSampling
1.3 OtherEffectiveSamplingMethods
1.4 SourcesofErrorsinSampling
1.5 TheDesignofExperiments
ChapterReview
"
CaseStudy:ChrysalisesforCash(onCD)
"
DECISIONS
ItisMondaymorningandalreadyyouarethinkingabout
Fridaynight—movienight.Youdon’ttrustthemoviereviews
publishedbyprofessionalcritics,soyoudecidetosurvey
“regular”peopleyourself.Youneedtodesignaquestionnaire
thatcanbeusedtohelpyoumakeaninformeddecisionabout
whethertoattendaparticularmovie.SeetheDecisionActivity
onpage37.
Putting ItAll Together
Formostofyou,thisisyourfirststatisticscourse.Taking whetheryouhavestruggledorhadsuccessinpriormath-
astatisticscourseisdifferentfromtakingamathematics ematicscourses,youcansucceedinstatistics.
course.Whilethereareformulasandmathematicalsym- Beforeyoubeginthecourse,read“HowtoUseThis
bols in the course, statistics is not mathematics. So, Book”ontheinsidefrontcoverofthetext.
2
Section1.1 IntroductiontothePracticeofStatistics 3
1.1 Introduction to the Practice of Statistics
Objectives Definestatisticsandstatisticalthinking
Understandtheprocessofstatistics
Distinguishbetweenqualitativeandquantitative
variables
Distinguishbetweendiscreteandcontinuousvariables
Define Statistics and Statistical Thinking
What is statistics?When asked this question,many people respond that statis-
ticsisnumbers.Thisresponseisonlypartiallycorrect.
Definition Statistics is the science of collecting,organizing,summarizing,and ana-
lyzinginformationtodrawconclusionsoranswerquestions.
Itishelpfultoconsiderthisdefinitioninthreeparts.Thefirstpartofthedef-
inition states that statistics involves the collection of information.The second
refers to the organization and summarization of information.Finally,the third
states that the information is analyzed to draw conclusions or answer specific
questions.
What is the information referred to in the definition? The information is
data.AccordingtotheAmericanHeritageDictionary,dataare“afactorpropo-
sitionusedtodrawaconclusionormakeadecision.”Datacanbenumerical,as
in height, or they can be nonnumerical, as in gender. In either case, data de-
scribecharacteristicsofanindividual.Thereasonthatdataareimportantinsta-
tisticscanbeseeninthisdefinition:dataareusedtodrawaconclusionormake
adecision.
Analysisofdatacanleadtopowerfulresults.Datacanbeusedtooffsetan-
ecdotalclaims,suchasthesuggestionthatcellulartelephonescausebraincan-
cer.After carefully collecting,summarizing,and analyzing data regarding this
phenomenon,itwasdeterminedthatthereisnolinkbetweencellphoneusage
andbraincancer.
In Other Words
Becausedataarepowerful,theycanbedangerouswhenmisused.Themis-
Anecdotalmeansthattheinformation
useofdatausuallyoccurswhendataareincorrectlyobtainedoranalyzed.For
beingconveyedisbasedoncasual
example,radioortelevisiontalkshowsregularlyaskpollquestionsinwhichre-
observation,notscientificresearch.
spondentsmustcallinorusetheInternettosupplytheirvote.Theonlyindivid-
uals who are going to call in are those that have a strong opinion about the
topic.This group is not likely to be representative of people in general,so the
resultsofthepollarenotmeaningful.Wheneverwelookatdata,weshouldbe
mindfulofwherethedatacomefrom.
Evenwhendatatellusthatarelationexists,weneedtoinvestigate.Forex-
ample,astudyshowedthatbreast-fedchildrenhavehigherIQsthanthosewho
werenotbreast-fed.Doesthisstudymeanthatmothersshouldbreast-feedtheir
children?Notnecessarily.ItmaybethatsomeotherfactorcontributestotheIQ
ofthechildren.Inthiscase,itturnsoutthatmotherswhobreast-feedgenerally
havehigherIQsthanthosewhodonot.Therefore,itmaybegeneticsthatleads
tothehigherIQ,notbreast-feeding.Thisillustratesanideainstatisticsknown
as the lurking variable.In statistics,we must consider the lurking variables be-
causetwovariablesmostoftenareinfluencedbyathirdvariable.Agoodstatis-
ticalstudywillhaveawayofdealingwiththelurkingvariable.
Another key aspect of data is that they vary.To help understand this vari-
ability,consider the students in your classroom.Is everyone the same height?
No.Doeseveryonehavethesamecolorhair?No.So,amongagroupofindivid-
uals there is variation.Now consider yourself.Do you eat the same amount of
foodeachday?No.Doyousleepthesamenumberofhourseachday?No.So,
4 Chapter1 DataCollection
evenlookingatanindividualthereisvariation.Datavary.Thegoalofstatistics
istodescribeandunderstandthesourcesofvariation.
Becauseofthisvariabilityindata,theresultsthatweobtainusingdatacan
vary.Thisisaverydifferentideathanwhatyoumaybeusedtofromyourmath-
ematics classes. In mathematics, if Bob and Jane are asked to solve
3x + 5 = 11,theywillbothobtainx = 2asthesolution,iftheyusethecorrect
procedures.Instatistics,ifBobandJaneareaskedtoestimatetheaveragecom-
mute time for workers in Dallas,Texas, they will likely get different answers,
even though they both use the correct procedure.The different answers occur
because they likely surveyed different individuals, and these individuals have
differentcommutetimes.Note:TheonlywayBobandJanewouldgetthesame
result is if they both asked all commuters or the same commuters how long it
takestogettowork,buthowlikelyisthis?
So,inmathematicswhenaproblemissolvedcorrectly,theresultscanbere-
ported with 100% certainty.In statistics,when a problem is solved,the results
do not have 100% certainty.In statistics,we might say that we are 95% confi-
dentthattheaveragecommutetimeinDallas,Texasis21.5minutes.Whileun-
certain results may sound disturbing now,it will become more apparent what
thismeansasweproceedthroughthecourse.
Withoutcertainty,howcanstatisticsbeuseful?Statisticscanprovideanun-
derstandingoftheworldaroundusbecauserecognizingwherevariabilityindata
comesfromcanhelpustocontrolit.Understandingthetechniquespresentedin
thistextwillprovideyouwithpowerfultoolsthatwillgiveyoutheabilitytoan-
alyzeandcritiquemediareports,makeinvestmentdecisions(suchaswhatmutu-
alfundtoinvestin),orconductresearchonmajorpurchases(suchaswhattype
ofcaryoushouldbuy).Thiswillhelptomakeyouaninformedconsumerofin-
formationandguideyouinbecomingacriticalandstatisticalthinker.
Understand the Process of Statistics
The definition of statistics implies that the methods of statistics follow a
process.
TheProcessofStatistics
1. Identify the research objective. A researcher must determine the ques-
tion(s)heorshewantsanswered.Thequestion(s)mustbedetailedsothat
itidentifiesagroupthatistobestudiedandthequestionsthataretobe
answered.Thegrouptobestudiediscalledthepopulation.Anindividual
isapersonorobjectthatisamemberofthepopulationbeingstudied.For
example,aresearchermaywanttostudythepopulationofall2005model-
CAUTION
yearautomobiles.Theindividualsinthisstudywouldbethecars.
Manynonscientificstudiesare 2. Collecttheinformationneededtoanswerthequestionsposedin(1).Gain-
basedonconveniencesamples,such ingaccesstoanentirepopulationisoftendifficultandexpensive.Incon-
asInternetsurveysorphone-inpolls. ductingresearch,wetypicallylookatasubsetofthepopulation,calleda
Theresultsofanystudyperformed sample.For example,the U.S.population of people 18 years or older is
usingthistypeofsamplingmethod about218million.Manynationalstudiesconsistofsamplesofsize1,100.
arenotreliable. The collection-of-information step is vital to the statistical process, be-
causeiftheinformationisnotcollectedcorrectly,theconclusionsdrawn
are meaningless. Do not overlook the importance of appropriate data-
collectionprocesses.
3. Organize and summarize the information.This step in the process is re-
ferredtoasdescriptivestatistics.
Definition Descriptive statistics consists of organizing and summarizing the in-
formationcollected.
Descriptivestatisticsdescribetheinformationcollectedthroughnumeri-
cal measurements, charts, graphs, and tables. The main purpose of de-
scriptivestatisticsistoprovideanoverviewoftheinformationcollected.
Section1.1 IntroductiontothePracticeofStatistics 5
4. Drawconclusionsfromtheinformation.Inthissteptheinformationcol-
lectedfromthesampleisgeneralizedtothepopulation.
Definition Inferential statistics uses methods that take results obtained from a
sample,extendsthemtothepopulation,andmeasuresthereliabilityofthe
result.
For example,if a researcher is conducting a study based on the popula-
tion ofAmericans aged 18 years or older,she might obtain a sample of
1,100 Americans aged 18 years or older.The results obtained from the
sample would be generalized to the population.There is always uncer-
tainty when using samples to draw conclusions regarding a population
because we can’t learn everything about a population by looking at a
sample.Therefore,statisticians will report a level of confidence in their
conclusions.Thislevelofconfidenceisawayofrepresentingthereliabili-
tyofresults.Iftheentirepopulationisstudied,theninferentialstatisticsis
not necessary,because descriptive statistics will provide all the informa-
tionthatweneedregardingthepopulation.
Thefollowingexamplewillillustratetheprocessofastatisticalstudy.
EXAMPLE 1 EffectivenessofAntihypertensiveDrugs
Accordingtoresearchers,littleinformationexistsontheeffectsthatantihyper-
tensivedrugshaveonpatientswhohaveheartdiseaseandnormalbloodpres-
sure.* Blood pressure is the force of blood against the walls of arteries and is
presentedastwonumbers:thesystolicpressure(astheheartbeats)overthedi-
astolic pressure (as the heart relaxes between beats).A blood pressure meas-
urementof120/80mmHg(millimetersofmercury)isnormal.Hypertensionor
high blood pressure exists in individuals with a systolic blood pressure above
160mmHgoradiastolicbloodpressureabove100mmHg.ResearchersSteven
E.Nissanandhisassociateswantedtodeterminetheeffectivenessofanantihy-
Group1 Group2
pertensivedrug**onpreventingcardiovasculareventssuchascongestiveheart
failure,stroke,orotherheart-relatedproblems.Thefollowingstatisticalprocess
allowedtheresearcherstomeasuretheeffectivenessofthedrug:
1. Identify the research objective.Researchers wished to determine the ef-
fectiveness of the drug on preventing cardiovascular events in patients
whohaveheartdiseaseandnormalbloodpressure.
2. Collect the information needed to answer the questions.The researchers
divided1,317patientswithheartdiseaseanddiastolicbloodpressureless
than100mmHgintotwogroups.Group1had663patientsandgroup2
had654patients.Thepatientsingroup1received10mgdailyoftheanti-
hypertensivedrug.Thepatientsingroup2receivedaplacebo.Aplacebo
isaninnocuousdrugsuchasasugartablet.Group1iscalledtheexperi-
mentalgroup.Group2iscalledthecontrolgroup.Neitherthedoctorad-
ministering the drug nor the patient knew whether he or she was in the
experimental or control group.This is referred to as a double-blind ex-
periment.After 24 months of treatment, each patient’s blood pressure
wasrecorded.Inaddition,thenumberofpatientsineachgroupwhoex-
periencedacardiovasculareventwascounted.
3. Organizeandsummarizetheinformation.Beforeadministeringanydrugs,
itwasdeterminedthatbothgroupshadsimilarbloodpressure.Afterthe
*ThediscussionisbasedonastudydonebyStevenE.Nissan,E.MuratTuzcu,PeterLibby,PaulD.
Thompson,Magdi Ghali,Dahlia Garza,Lance Berman,Harry Shi,Ethel Buebendorf,and Eric
TopolpublishedintheJournaloftheAmericanMedicalAssociation,Vol.292,No.18.
**Thedrugusedinthestudywas10mgofamlodipine.
6 Chapter1 DataCollection
24-month period ended, the experimental group’s blood pressure de-
creasedby4.8/2.5mmHg,whereastheplacebogroup’sbloodpressurein-
creased0.7/0.6mmHg.Inaddition,16.6%ofpatientsintheexperimental
groupexperiencedacardiovascularevent,while23.1%ofpatientsinthe
control(placebo)groupexperiencedacardiovascularevent.
4. Drawconclusionsfromthedata.Weextendtheresultsfromthesampleof
1,317patientstoallindividualswhohaveheartdiseaseandnormalblood
pressure. That is, the antihypertensive drug appears to decrease blood
pressureandseemseffectiveinreducingthelikelihoodofexperiencinga
cardiovasculareventsuchasastroke.
In the study presented in Example 1,notice that the population is clearly
identifiedintheresearchobjectiveaspatientswhohaveheartdiseaseandnor-
mal blood pressure. However, the researchers collected the information that
theyneededbylookingatasubsetofthispopulation,the1,317patients.
NowWorkProblem45.
Distinguish between Qualitative
and Quantitative Variables
Oncearesearchobjectiveisstated,alistoftheinformationtheresearcherde-
sires about the individual must be created.Variables are the characteristics of
theindividualswithinthepopulation.Forexample,thispastspringmysonand
I planted a tomato plant in our backyard.We decided to collect some infor-
mationaboutthetomatoesharvestedfromtheplant.Theindividualswestud-
ied were the tomatoes.The variable that interested us was the weight of the
tomatoes.Mysonnotedthatthetomatoeshaddifferentweightseventhough
they all came from the same plant. He discovered that variables such as
weightvary.
If variables did not vary,they would be constants,and statistical inference
wouldnotbenecessary.Thinkaboutitthisway:Ifallthetomatoeshadthesame
weight, then knowing the weight of one tomato would be sufficient to deter-
minetheweightsofalltomatoes.However,theweightsoftomatoesvaryfrom
onetomatotothenext.Onegoalofresearchistolearnthecausesofthevari-
abilitysothatwecanlearntogrowplantsthatyieldthebesttomatoes.
Variablescanbeclassifiedintotwogroups:qualitativeorquantitative.
Definition Qualitativeorcategoricalvariablesallowforclassificationofindi-
vidualsbasedonsomeattributeorcharacteristic.
Quantitative variables provide numerical measures of individuals.
Arithmetic operations such as addition and subtraction can be performed
onthevaluesofaquantitativevariableandwillprovidemeaningfulresults.
Many examples in this text will include a suggested approach,or a way to
lookatandorganizeaproblemsothatitcanbesolved.Theapproachwillbea
suggested method of attack toward solving the problem.This does not mean
that the approach given is the only way to solve the problem, because many
problems have more than one approach leading to a correct solution.For ex-
In Other Words ample,if you turn the key on your car’s ignition and it doesn’t start,one ap-
Typically,thereismorethanone proach would be to look under the hood and try to determine what is wrong.
correctapproachtosolvingaproblem. (Ofcourse,thisapproachwouldworkonlyifyouknowhowtofixcars.)Asec-
ond,equallyvalidapproachwouldbetocallanautomobilemechanictoservice
thecar.
Section1.1 IntroductiontothePracticeofStatistics 7
EXAMPLE 2 DistinguishingbetweenQualitativeandQuantitative
Variables
Problem: Determinewhetherthefollowingvariablesarequalitativeorquan-
titative.
(a) Gender
(b) Temperature
(c) Number of days during the past week a college student aged 21 years or
olderhashadatleastonedrink
(d) Zipcode
Approach: Quantitative variables are numerical measures such that arith-
metic operations can be performed on the values of the variable. Qualitative
variablesdescribeanattributeorcharacteristicoftheindividualthatallowsre-
searcherstocategorizetheindividual.
Solution
(a) Genderisaqualitativevariablebecauseitallowsaresearchertocategorize
the individual as male or female.Notice that arithmetic operations cannot
beperformedontheseattributes.
(b) Temperatureisaquantitativevariablebecauseitisnumeric,andoperations
such as addition and subtraction provide meaningful results.For example,
70°Fis10°Fwarmerthan60°F.
(c) Numberofdaysduringthepastweekthatacollegestudentaged21years
or older had at least one drink is a quantitative variable because it is nu-
meric,andoperationssuchasadditionandsubtractionprovidemeaningful
results.
(d) Zip code is a qualitative variable because it categorizes a location.Notice
that the addition or subtraction of zip codes does not provide meaningful
NowWorkProblem15. results.
OnthebasisoftheresultofExample2(d),weconcludethatavariablemay
bequalitativewhilehavingvaluesthatarenumeric.Justbecausethevalueofa
variableisnumericdoesnotmeanthatthevariableisquantitative.
Distinguish between Discrete and Continuous
Variables
Wecanfurtherclassifyquantitativevariablesintotwotypes.
Definition A discrete variable is a quantitative variable that has either a finite
number of possible values or a countable number of possible values.The
In Other Words termcountablemeansthatthevaluesresultfromcounting,suchas0,1,2,3,
andsoon.
Ifyoucounttogetthevalueofa
variable,itisdiscrete.Ifyoumeasureto A continuous variable is a quantitative variable that has an infinite
getthevalueofthevariable,itis numberofpossiblevaluesthatarenotcountable.
continuous.Whendecidingwhethera
variableisdiscreteorcontinuous,ask
Figure 1 illustrates the relationship among qualitative, quantitative, discrete,
yourselfifitiscountedormeasured.
andcontinuousvariables.
Figure1
Qualitative Quantitative
variables variables
Discrete Continuous
variables variables
8 Chapter1 DataCollection
Recognizingthetypeofvariablebeingstudiedisimportantbecauseitdic-
tates the type of analysis that can be performed.An example should help to
clarifythedefinitions.
EXAMPLE 3 DistinguishingbetweenDiscreteandContinuous
Variables
Problem: Determine whether the following quantitative variables are dis-
creteorcontinuous.
(a) Thenumberofheadsobtainedafterflippingacoinfivetimes.
(b) The number of cars that arrive at a McDonald’s drive-through between
12:00P.Mand1:00P.M.
(c) Thedistancea2005ToyotaPriuscantravelincitydrivingconditionswitha
fulltankofgas.
Approach: Avariableisdiscreteifitsvalueresultsfromcounting.Avariable
iscontinuousifitsvalueismeasured.
Solution
(a) Thenumberofheadsobtainedbyflippingacoinfivetimeswouldbeadis-
cretevariablebecausewewouldcountthenumberofheadsobtained.The
possiblevaluesofthediscretevariableare0,1,2,3,4,5.
(b) ThenumberofcarsthatarriveatMcDonald’sdrive-throughbetween12:00
P.M.and1:00P.M.isadiscretevariablebecauseitsvaluewouldresultfrom
countingthecars.Thepossiblevaluesofthediscretevariableare0,1,2,3,4,
andsoon.Noticethatthereisnopredeterminedupperlimittothenumber
ofcarsthatmayarrive.
(c) Thedistancetraveledisacontinuousvariablebecausewemeasurethedis-
tance.
Continuous variables are often rounded.For example,when the miles per
gallon(mpg)ofgasolineforacertainmakeofcarisgivenas24mpg,itmeans
that the miles per gallon is greater than or equal to 23.5 and less than 24.5,or
23.5 … mpg 6 24.5.
NowWorkProblem27.
The list of observed values for a variable is data.Gender is a variable,the
observations male or female are data. Qualitative data are observations
In Other Words
correspondingtoaqualitativevariable.Quantitativedataareobservationscor-
Thesingularofdataisdatum. respondingtoaquantitativevariable.Discretedataareobservationscorresponding
to a discrete variable,and continuous data are observations corresponding to a
continuousvariable.
EXAMPLE 4 DistinguishingbetweenVariablesandData
Problem: Table1presentsagroupofselectedcountriesandinformationre-
garding these countries as of July,2004.Identify the individuals,variables,and
datainTable1.
Approach: Anindividualisanobjectorpersonforwhomwewishtoobtain
data.Thevariablesarethecharacteristicsoftheindividuals,andthedataarethe
specificvaluesofthevariables.
Solution: The individuals in the study are the countries:Australia, Canada,
andsoon(inredink).Thevariablesmeasuredforeachcountryaregovernment
type,lifeexpectancy,andpopulation(inblueink).Thevariablegovernmenttype
is qualitative because it categorizes the individual.The quantitative variables
arelifeexpectancyandpopulation.
Section1.1 IntroductiontothePracticeofStatistics 9
Table 1
Life
Government Expectancy Population
Country Type (years) (inmillions)
Australia Democratic 80.26 19.9
Canada Confederation 79.96 32.5
France Republic 79.44 60.4
Morocco ConstitutionalMonarchy 70.35 32.2
Poland Republic 74.16 38.6
SriLanka Republic 72.89 19.9
UnitedStates FederalRepublic 77.43 293.0
Source:CIAWorldFactbook
The quantitative variable life expectancy is continuous because it is meas-
ured.Thequantitativevariablepopulationisdiscretebecausewecountpeople.
The observations are the data (in green ink).For example,the data correspon-
dingtothevariablelifeexpectancyare80.26,79.96,79.44,70.35,74.16,72.89,and
77.43.ThefollowingdatacorrespondtotheindividualPoland:arepublicgovern-
mentwithresidentswhoselifeexpectancyis74.16yearsandwherepopulationis
38.6millionpeople.Republicisaninstanceofqualitativedatathatresultsfrom
observing the value of the qualitative variable government type. The life ex-
pectancyof74.16yearsisaninstanceofquantitativedatathatresultsfromob-
servingthevalueofthequantitativevariablelifeexpectancy.
NowWorkProblem51.
1.1 ASSESSYOUR UNDERSTANDING
ConceptsandVocabulary
1. Definestatistics. 8. Whatareplacebos?Whydoyouthinktheyareneeded?
2. Explainthedifferencebetweenapopulationanda 9. _____arethecharacteristicsoftheindividualsofthepop-
sample. ulationbeingstudied.
3. Statisticsisthescienceofcollecting,organizing,summa- 10. Contrastthedifferencesbetweenqualitativeandquanti-
rizing,andanalyzing_____toanswerquestionsordraw tativevariables.
conclusions. 11. Discussthedifferencebetweendiscreteandcontinuous
4. A(n)_____isapersonorobjectthatisamemberofthe variables.
populationbeingstudied. 12. TrueorFalse:Bothdiscreteandcontinuousvariablesare
5. _____statisticsconsistsoforganizingandsummarizing quantitativevariables.
informationcollected,while_____statisticsusesmethods 13. Explaintheprocessofstatistics.
thatgeneralizeresultsobtainedfromasampletothe 14. Theageofapersoniscommonlyconsideredtobeacon-
populationandmeasurethereliabilityoftheresults. tinuousrandomvariable.Coulditbeconsideredadis-
6. Whatdoesitmeanwhenanexperimentisdouble-blind? creterandomvariableinstead?Explain.
7. Discussthedifferencesbetweenanexperimentalgroup
andacontrolgroup.
SkillBuilding
InProblems15–26,classifythevariableasqualitativeorquantitative.
15. Nationoforigin 21. Assessedvalueofahouse
NW
22. Phonenumber
16. Numberofsiblings
23. Populationofastate
17. Eyecolor
24. Cost(indollars)tofillupa2005ChevroletCorvette
18. Numberonafootballplayer’sjersey
25. StudentIDnumber
19. Gramsofcarbohydratesinadoughnut
26. Maritalstatus
20. NumberofunpoppedkernelsinabagofACTmicrowave
popcorn
10 Chapter1 DataCollection
InProblems27–38,determinewhetherthequantitativevariableisdiscreteorcontinuous.
27. RunsscoredinaseasonbyAlbertPujols 34. Internetconnectionspeedinkilobytespersecond
NW
35. NumberoftornadoesinayearintheUnitedStates
28. Volumeofwaterlosteachdaythroughaleakyfaucet
29. Lengthofacountrysong 36. PointsscoredinanNCAAbasketballgame
30. Atrestpulserateofa20-year-oldcollegestudent
37. Numberofdonorsatablooddrive
31. Number of sequoia trees in a randomly selected acre of
38. Airpressureinpoundspersquareinchinanautomobiletire
YosemiteNationalPark
32. Weightofarandomlyselectedhog
33. Temperature on a randomly selected day in Memphis,
Tennessee
InProblems39–44,aresearchobjectiveispresented.Foreachresearchobjective,identifythepopulationandsampleinthestudy.
39. TheGallupOrganizationcontacts1,028teenagerswhoare lateintakeisassociatedwithalowerriskofhypertension
13to17yearsofageandliveintheUnitedStatesandasked (highbloodpressure)inyoungerwomen(27to44yearsof
whether or not they had been prescribed medications for age). To make this determination, they looked at 7,373
anymentaldisorders,suchasdepressionoranxiety. cases of hypertension in younger women and found that
youngerwomenwhoconsumedatleast1,000micrograms
40. Aquality-controlmanagerrandomlyselects50bottlesof
perday1mg/d2oftotalfolate(dietaryplussupplemental)
Coca-ColathatwerefilledonOctober15toassessthecal-
hadadecreasedriskofhypertensioncomparedwiththose
ibrationofthefillingmachine.
whoconsumedlessthan200mg/d.
41. Afarmerwantedtolearnabouttheweightofhissoybean
(Source:“Folateintakeandtheriskofincidenthyperten-
crop.He randomly sampled 100 plants and weighed the
sion among US Women,” John P. Forman, MD; Eric B.
soybeansoneachplant.
Rimm,ScD;MeirJ.Stampfer,MD;GaryC.Curhan,MD,
42. Every year the U.S.Census Bureau releases the Current ScD; Journal of the American Medical Association
Population Report based on a survey of 50,000 house- 293(2005):320–329)
holds.Thegoalofthisreportistolearnthedemographic
44. Alargecommunitycollegehasnoticedthatanincreasing
characteristicsofallhouseholdswithintheUnitedStates,
numberoffull-timestudentsareworkingwhileattending
suchasincome.
the school.The administration randomly selects 128 stu-
43. FolateandHypertension ResearcherJohnP.Formanand dents and asks this question:How many hours per week
co-workerswantedtodeterminewhetherornothigherfo- doyouwork?
ApplyingtheConcepts
For the studies in Problems 45–50,(a) identify the research objective,(b) identify the sample,(c) list the descriptive statistics,and
(d)statetheconclusionsmadeinthestudy.
45. ACurefortheCommonWart Astudyconductedbyre- 46. EarlyEpidurals AstudywasconductedatNorthwestern
NWsearchers was designed “to determine if application of UniversityinChicagotodetermineifpregnantwomenin
ducttapeisaseffectiveascryotherapyinthetreatmentof first-timelaborcouldreceivelow-doseepidurals,ananes-
commonwarts.”Theresearchersrandomlydivided51pa- thesistocontrolpainduringchildbirthearlywithoutrais-
tientsintotwogroups.The26patientsingroup1hadtheir ing their chances of a Caesarean section. In the study,
warts treated by applying duct tape to the wart for 6.5 reported in the New England Journal of Medicine,“728
days and then removing the tape for 12 hours,at which women in first-time labor were divided into two groups.
pointthecyclewasrepeatedforamaximumof2months. Onegroupreceivedthespinalshotandthengotepidurals
The 25 patients in group 2 had their warts treated by whenthecervixdilatedtoabout2centimeters.Theother
cryotherapy (liquid nitrogen applied to the wart for 10 group initially received pain-relieving medicine directly
seconds every 2 to 3 weeks) for a maximum of 6 treat- intotheirbloodstreams,andputoffepiduralsuntil4cen-
ments.Once the treatments were complete,it was deter- timetersiftheycouldtoleratethepain.”Intheend,theC-
minedthat85%ofthepatientsingroup1and60%ofthe sectionratewas18%intheearlyepiduralgroupand21%
patientsingroup2hadcompleteresolutionoftheirwarts. inthedelayedgroup.Theresearchersconcludedthatpreg-
The researchers concluded that duct tape is significantly nant women in first-time labor can be given a low-dose
moreeffectiveintreatingwartsthancryotherapy. epiduralearlywithoutraisingtheirchancesofaC-section.
(Source: “The Efficacy of Duct Tape vs. Cryotherapy in (Source:AssociatedPress,Feb.22,2005)
theTreatmentofVerrucaVulgaris(TheCommonWart),”
47. TheMozartEffect ResearchersattheUniversityofCali-
Dean R. Focht III, Carole Spicer, Mary P. Fairchok;
fornia,Irvine,wishedtodeterminewhether“musiccogni-
Archives of Pediatrics andAdolescent Medicine,Vol.156,
tionandcognitionspertainingtoabstractoperationssuch
No.10,October2002)
asmathematicalorspatialreasoning”wererelated.Totest