Chapter 08 Find The Standardized Test Statistic Test The

Unlock access to all the studying documents.

View Full Document

Ch.8 HypothesisTestingwithTwoSamples

8.1 TestingtheDifferenceBetweenMeans(LargeIndependentSamples)

1 DeterminetheDifferenceBetweenDependentandIndependentSamples

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Classifythetwogivensamplesasindependentordependent.

Sample1:Pre–trainingweightsof19people

Sample2:Post–trainingweightsof19people

A) dependent B) independent

2) Classifythetwogivensamplesasindependentordependent.

Sample1:Theweightsinpoundsof26newbornfemales

Sample2:Theweightsinpoundsof26newbornmales

A) independent B) dependent

3) Classifythetwogivensamplesasindependentordependent.

Sample1:Thescoresof10studentswhotooktheACT

Sample2:Thescoresof10differentstudentswhotooktheSAT

A) independent B) dependent

4) Aspartofamarketingexperiment,adepartmentstoreregularlymaileddiscountcouponsto25ofitscredit

cardholders.Theirtotalcreditcardpurchasesoverthenextthreemonthswerecomparedtotheirpriorcredit

cardpurchasesduringthepreviousthreemonths.Determinewhetherthesamplesaredependentor

independent.

A) dependent B) independent

5) Aspartofamarketingexperiment,adepartmentstoreregularlymaileddiscountcouponsto25ofitscredit

cardholders.Theirtotalcreditcardpurchasesoverthenextthreemonthswerecomparedtothecreditcard

purchasesoverthenextthreemonthsfor25creditcardholderswhowerenotsentdiscountcoupons.

Determinewhetherthesamplesaredependentorindependent.

A) independent B) dependent

6) AspartofaMasterʹsthesisproject,amathematicsteacherisinterestedintheeffectsoftwodifferentteaching

methodsonmathematicsachievement.Sherandomlychoosesoneclassofstudentstolearnanalgebraic

conceptusingtraditionalmethodsandanotherclassofstudentstolearnthesamealgebraicconceptusing

manipulatives.Theteacherthencomparestheirtestscores.Determinewhetherthesamplesaredependentor

independent.

A) independent B) dependent

7) AspartofaMasterʹsthesisproject,amathematicsteacherisinterestedintheeffectsoftwodifferentteaching

methodsonmathematicsachievement.Sherandomlychoosesaclassofstudentstolearnonealgebraicconcept

usingtraditionalmethods.Thenonanotherday,thesamestudentslearnasimilaralgebraicconceptusing

manipulatives.Theteacherthencomparestheirtestscores.Determinewhetherthesamplesaredependentor

independent.

A) dependent B) independent

Page151

2 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

8) Findthestandardizedteststatistictotesttheclaimthatμ1=μ2.Twosamplesarerandomlyselectedfromeach

population.Thesamplestatisticsaregivenbelow.

n1=50 n2=60

x1=21 x2=19

s1=1.5 s2=1.9

A) 6.2 B) 8.1 C) 4.2 D) 3.8

9) Findthestandardizedteststatistictotesttheclaimthatμ1=μ2.Twosamplesarerandomlyselectedfromeach

population.Thesamplestatisticsaregivenbelow.

n1=40n2=35

x1=21 x2=22

s1=2.5s2=2.8

A) –1.6 B) –0.8 C) –2.6 D) –1.0

10) Findthestandardizedteststatistictotesttheclaimthatμ1>μ2.Twosamplesarerandomlyselectedfromeach

population.Thesamplestatisticsaregivenbelow.

n1=100n2=125

x1=465 x2=450

s1=45s2=25

A) 2.99 B) 2.81 C) 1.86 D) 0.91

11) Findthestandardizedteststatistictotesttheclaimthatμ1<μ2.Twosamplesarerandomlyselectedfromeach

population.Thesamplestatisticsaregivenbelow.

n1=35n2=42

x1=23.97 x2=26.52

s1=2.9s2=2.8

A) –3.90 B) –3.16 C) –2.63 D) –1.66

12) Findthestandardizedteststatistictotesttheclaimthatμ1≠μ2.Twosamplesarerandomlyselectedfromeach

population.Thesamplestatisticsaregivenbelow.

n1=51n2=38

x1=1.4 x2=1.8

s1=0.76s2=0.51

A) –2.97 B) –1.82 C) –2.12 D) –2.32

Page152

13) Supposeyouwanttotesttheclaimthatμ1≠μ2.Twosamplesarerandomlyselectedfromeachpopulation.

Thesamplestatisticsaregivenbelow.Atalevelofsignificanceofα

=0.05,whenshouldyourejectH0?

n1=50n2=60

x1=19 x2=17

s1=1.5s2=1.9

A) RejectH0ifthestandardizedteststatisticislessthan–1.96orgreaterthan1.96.

B) RejectH0ifthestandardizedteststatisticislessthan–2.33orgreaterthan2.33.

C) RejectH0ifthestandardizedteststatisticislessthan–1.645orgreaterthan1.645.

D) RejectH0ifthestandardizedteststatisticislessthan–2.575orgreaterthan2.575.

14) Supposeyouwanttotesttheclaimthatμ1=μ2.Twosamplesarerandomlyselectedfromeachpopulation.Ifa

hypothesistestisperformed,howshouldyouinterpretadecisionthatrejectsthenullhypothesis?

A) Thereissufficientevidencetorejecttheclaimμ1=μ2.

B) Thereisnotsufficientevidencetorejecttheclaimμ1=μ2.

C) Thereissufficientevidencetosupporttheclaimμ1=μ2.

D) Thereisnotsufficientevidencetosupporttheclaimμ1=μ2.

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

15) Testtheclaimthatμ1=μ2.Twosamplesarerandomlyselectedfromeachpopulation.Thesamplestatisticsare

givenbelow.Useα=0.05.

n1=50n2=60

x1=31 x2=29

s1=1.5s2=1.9

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

16) Supposeyouwanttotesttheclaimthatμ1>μ2.Twosamplesarerandomlyselectedfromeachpopulation.

Thesamplestatisticsaregivenbelow.Atalevelofsignificanceofα

=0.01,whenshouldyourejectH0?

n1=100n2=125

x1=690 x2=675

s1=45s2=25

A) RejectH0ifthestandardizedteststatisticisgreaterthan2.33.

B) RejectH0ifthestandardizedteststatisticisgreaterthan1.96.

C) RejectH0ifthestandardizedteststatisticisgreaterthan1.645.

D) RejectH0ifthestandardizedteststatisticisgreaterthan2.575.

17) Supposeyouwanttotesttheclaimthatμ1>μ2.Twosamplesarerandomlyselectedfromeachpopulation.Ifa

hypothesistestisperformed,howshouldyouinterpretadecisionthatrejectsthenullhypothesis?

A) Thereissufficientevidencetosupporttheclaimμ1>μ2.

B) Thereissufficientevidencetorejecttheclaimμ1>μ2.

C) Thereisnotsufficientevidencetorejecttheclaimμ1>μ2.

D) Thereisnotsufficientevidencetosupporttheclaimμ1>μ2.

Page153

18) Supposeyouwanttotesttheclaimthatμ1<μ2.Twosamplesarerandomlyselectedfromeachpopulation.

Thesamplestatisticsaregivenbelow.Atalevelofsignificanceofα

=0.05,whenshouldyourejectH0?

n1=35n2=42

x1=29.23 x2=31.78

s1=2.9s2=2.8

A) RejectH0ifthestandardizedteststatisticislessthan–1.645.

B) RejectH0ifthestandardizedteststatisticislessthan–1.96.

C) RejectH0ifthestandardizedteststatisticislessthan–2.33.

D) RejectH0ifthestandardizedteststatisticislessthan–2.575.

19) Supposeyouwanttotesttheclaimthatμ1<μ2.Twosamplesarerandomlyselectedfromeachpopulation.Ifa

hypothesistestisperformed,howshouldyouinterpretadecisionthatfailstorejectthenullhypothesis?

A) Thereisnotsufficientevidencetosupporttheclaimμ1<μ2.

B) Thereissufficientevidencetorejecttheclaimμ1<μ2.

C) Thereisnotsufficientevidencetorejecttheclaimμ1<μ2.

D) Thereissufficientevidencetosupporttheclaimμ1<μ2.

20) Supposeyouwanttotesttheclaimthatμ1≠μ2.Twosamplesarerandomlyselectedfromeachpopulation.

Thesamplestatisticsaregivenbelow.Atalevelofsignificanceofα

=0.02,whenshouldyourejectH0?

n1=51n2=38

x1=8.6 x2=9

s1=0.76s2=0.51

A) RejectH0ifthestandardizedteststatisticislessthan–2.33orgreaterthan2.33.

B) RejectH0ifthestandardizedteststatisticislessthan–1.96orgreaterthan1.96.

C) RejectH0ifthestandardizedteststatisticislessthan–1.645orgreaterthan1.645.

D) RejectH0ifthestandardizedteststatisticislessthan–2.575orgreaterthan2.575.

21) Supposeyouwanttotesttheclaimthatμ1≠μ2.Twosamplesarerandomlyselectedfromeachpopulation.Ifa

hypothesistestisperformed,howshouldyouinterpretadecisionthatfailstorejectthenullhypothesis?

A) Thereisnotsufficientevidencetosupporttheclaimμ1≠μ2.

B) Thereissufficientevidencetorejecttheclaimμ1≠μ2.

C) Thereisnotsufficientevidencetorejecttheclaimμ1≠μ2.

D) Thereissufficientevidencetosupporttheclaimμ1≠μ2.

22) Twosamplesarerandomlyselectedfromeachpopulation.Thesamplestatisticsaregivenbelow.Findthe

P–valueusedtotesttheclaimthatμ1=μ2.Useα=0.05.

n1=40n2=35

x1=12x2=13

s1=2.5s2=2.8

A) 0.1052 B) 0.0526 C) 0.4020 D) 0.1138

Page154

23) Twosamplesarerandomlyselectedfromeachpopulation.Thesamplestatisticsaregivenbelow.Findthe

P–valueusedtotesttheclaimthatμ1>μ2.Useα=0.05.

n1=100n2=125

x1=615x2=600

s1=40s2=24

A) 0.0005 B) 0.0505 C) 0.1015 D) 0.5105

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

24) Testtheclaimthatμ1>μ2.Twosamplesarerandomlyselectedfromeachpopulation.Thesamplestatisticsare

givenbelow.Useα=0.01.

n1=100n2=125

x1=455 x2=440

s1=45s2=25

25) Testtheclaimthatμ1<μ2.Twosamplesarerandomlyselectedfromeachpopulation.Thesamplestatisticsare

givenbelow.Useα=0.05.

n1=35n2=42

x1=25.79 x2=28.34

s1=2.9s2=2.8

26) Testtheclaimthatμ1≠μ2.Twosamplesarerandomlyselectedfromeachpopulation.Thesamplestatisticsare

givenbelow.Useα=0.02.

n1=51n2=38

x1=7.9 x2=8.3

s1=0.76s2=0.51

27) Astudywasconductedtodetermineifthesalariesofelementaryschoolteachersfromtwoneighboringstates

wereequal.Asampleof100teachersfromeachstatewasrandomlyselected.Themeanfromthefirststatewas

$28,700withastandarddeviationof$2300.Themeanfromthesecondstatewas$30,100withastandard

deviationof$2100.Testtheclaimthatthesalariesfrombothstatesareequal.Useα=0.05.

28) Atalocalcollege,65femalestudentswererandomlyselectedanditwasfoundthattheirmeanmonthlyincome

was$609withastandarddeviationof$121.50.Seventy–fivemalestudentswerealsorandomlyselectedand

theirmeanmonthlyincomewasfoundtobe$651withastandarddeviationof$168.70.Testtheclaimthatmale

studentshaveahighermonthlyincomethanfemalestudents.Useα=0.01.

29) Amedicalresearchersuspectsthatthepulserateofsmokersishigherthanthepulserateofnon–smokers.Use

thesamplestatisticsbelowtotesttheresearcherʹssuspicion.Useα=0.05.

SmokersNonsmokers

n1=100n2=100

x1=86x2=83

s1=4.8s2=5.3

Page155

30) Astatisticsteacherbelievesthatstudentsinaneveningstatisticsclassscorehigherthanthestudentsinaday

class.Theresultsofaspecialexamareshownbelow.Cantheteacherconcludethattheeveningstudentshavea

higherscore?Useα=0.01.

DayStudentsEveningStudents

n1=36 n2=41

x1=96 x2=99

s1=5.8 s2=6.3

31) Astatisticsteacherwantedtoseewhethertherewasasignificantdifferenceinagesbetweendaystudentsand

nightstudents.Arandomsampleof35studentsisselectedfromeachgroup.Thedataaregivenbelow.Testthe

claimthatthereisnodifferenceinagebetweenthetwogroups.Useα=0.05.

DayStudents

222424231919232218212118

182529242322222120202027

1719182120232630252125

EveningStudents

182325232121232427312420

202319252427232020212524

2328201923242027212930

32) Alocalbankclaimsthatthewaitingtimeforitscustomerstobeservedisthelowestinthearea.Acompetitor

bankchecksthewaitingtimesatbothbanks.Thesamplestatisticsarelistedbelow.Testthelocalbankʹsclaim.

Useα=0.05.

LocalBankCompetitorBank

n1=45 n2=50

x1=4.7minutes x2=5minutes

s1=1.1minutess2=1.0minute

33) Alocalbankclaimsthatthewaitingtimeforitscustomerstobeservedisthelowestinthearea.Acompetitor

bankchecksthewaitingtimesatbothbanks.Thesamplestatisticsarelistedbelow.UseP–valuestotestthe

localbankʹsclaim.Useα=0.05.

LocalBankCompetitorBank

n1=45n2=50

x1=5.3minutesx2=5.6minutes

s1=1.1minutess2=1.0minutes

Page156

34) AfinancialadvisorwantstoknowwhetherthereisasignificantdifferencebetweentheNYSEandNASDAQ

marketsintheannualdividendratesforpreferredstocks.Arandomsampleof30returnsisselectedfromeach

market.Thedataaregivenbelow.Testtheclaimthatthereisnodifferenceintheannualdividendratesforthe

twomarkets.Useα=0.05.

NASDAQ

2.00 1.02 2.11 2.56 2.15 0.93 0.91 1.67 1.88 2.13

2.44 1.97 2.00 1.81 2.25 1.72 1.75 1.05 0.90 2.34

0.51 1.00 2.25 0.85 1.50 2.33 1.59 2.25 0.23 1.63

NYSE

1.46 3.00 1.74 5.19 1.69 1.88 2.85 2.00 2.19 2.03

1.81 5.00 1.72 3.38 2.09 4.50 3.07 1.97 1.78 1.50

1.97 4.65 3.12 2.19 2.19 3.50 1.56 4.10 3.00 4.40

35) Arecentstudyof100elementaryschoolteachersinasouthernstatefoundthattheirmeansalarywas$23,400

withastandarddeviationof$2100.Asimilarstudyof100elementaryschoolteachersinawesternstatefound

thattheirmeansalarywas$33,800withastandarddeviationof$3200.Testtheclaimthatthesalariesof

elementaryschoolteachersinthewesternstateismorethan$10,000greaterthanthatofelementaryteachersin

thesouthernstate.Useα=0.05.

36) Atα=0.05,testafinancialadvisorʹsclaimthatthedifferencebetweenthemeandividendrateforlistingsinthe

NYSEmarketandthemeandividendrateforlistingsintheNASDAQmarketismorethan0.75.Thesample

statisticsfromrandomlyselectedlistingsfromeachmarketarelistedbelow.

NYSE NASDAQ

n1=30 n2=50

x1=2.75% x2=1.66%

s1=1.14% s2=0.63%

37) Twogroupsofpatientswithcolorectalcanceraretreatedwithadifferentdrugtoreducepain.Arandom

sampleof140patientsaretreatedusingthedrugIrinoticanandarandomsampleof127patientsaretreated

usingthedrugFluorouracil.Thesamplestatisticsarelistedbelow.Atα=0.01,testapharmaceutical

representativeʹsclaimthatthedifferencebetweenthemeannumberofpain–freemonthsforpatientsusing

Fluorouracilandthemeannumberofpain–freemonthsforpatientsusingIrinoticanislessthantwomonths.

Fluorouracil Irinotican

n1=127 n2=140

x1=8.5months x2=10.3months

s1=1.5months s2=1.2months

Page157

3 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

38) Alocalbankclaimsthatthewaitingtimeforitscustomerstobeservedisthelowestinthearea.Acompetitor

bankchecksthewaitingtimesatbothbanks.Thesamplestatisticsarelistedbelow.Useα

=0.05anda

confidenceintervaltotestthelocalbankʹsclaim.

LocalBank CompetitorBank

n1=45 n2=50

x1=5.3minutes x2=5.6minutes

s1=1.1minutes s2=1.0minute

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

39) Constructa95%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromeachpopulation.

Thesamplestatisticsaregivenbelow.

n1=50n2=60

x1=25x2=23

s1=1.5s2=1.9

A) (1.364,2.636) B) (1.572,2.987) C) (1.723,3.012) D) (1.919,3.142)

40) Constructa95%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromeachpopulation.

Thesamplestatisticsaregivenbelow.

n1=40n2=35

x1=12x2=13

s1=2.5s2=2.8

A) (–2.209,0.209) B) (–2.001,–1.873) C) (–1.968,1.561) D) (–1.673,1.892)

41) Forwhichconfidenceintervalforthedifferenceinthemeansμ1–μ2

wouldyourejectthenullhypothesis?

A) (–2.001,–1.873) B) (–1.968,1.561) C) (–1.673,1.892) D) (–2.209,0.209)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

42) Aresearcherwishestodeterminewhetherpeoplewithhighbloodpressurecanlowertheirbloodpressureby

followingacertaindiet.Atreatmentgroupandacontrolgroupareselected.Thesamplestatisticsaregiven

below.Constructa90%confidenceintervalforthedifferencebetweenthetwopopulationmeans,μ

1–μ2.

Wouldyourecommendusingthisdietplan?Explainyourreasoning.

TreatmentGroupControlGroup

n1=100n2=100

x1=178x2=193

s1=35s2=37

Page158

8.2 TestingtheDifferenceBetweenMeans(SmallIndependentSamples)

1 FindCriticalValues

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Findthecriticalvalues,t0

totesttheclaimthatμ1=μ2.Twosamplesarerandomlyselectedandcomefrom

populationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.

Useα=0.05.

n1=25n2=30

x1=29 x2=27

s1=1.5 s2=1.9

A) ±2.064 B) ±2.797 C) ±1.711 D) ±2.492

2) Findthecriticalvalues,t0

totesttheclaimthatμ1=μ2.Twosamplesarerandomlyselectedandcomefrom

populationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Useα=0.05.

n1=14n2=12

x1=21 x2=22

s1=2.5 s2=2.8

A) ±2.064 B) ±2.492 C) ±1.711 D) ±1.318

3) Findthecriticalvalue,t0

totesttheclaimthatμ1>μ2.Twosamplesarerandomlyselectedandcomefrom

populationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Useα=0.01.

n1=18 n2=13

x1=785 x2=770

s1=40s2=25

A) 2.681 B) 1.699 C) 2.179 D) 3.055

4) Findthecriticalvalue,t0

totesttheclaimthatμ1<μ2.Twosamplesarerandomlyselectedandcomefrom

populationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Useα=0.05.

n1=15n2=15

x1=25.59 x2=28.14

s1=2.9s2=2.8

A) –1.701 B) 2.467 C) –1.313 D) 0.683

Page159

5) Findthecriticalvalue,t0

totesttheclaimthatμ1≠μ2.Twosamplesarerandomlyselectedandcomefrom

populationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Useα=0.02.

n1=11n2=18

x1=3.2 x2=3.6

s1=0.76 s2=0.51

A) ±2.764 B) ±0.684 C) ±2.228 D) ±3.169

2 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

6) Findthestandardizedteststatistic,t,totesttheclaimthatμ1=μ2.Twosamplesarerandomlyselectedand

comefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1≠σ 2

n1=25n2=30

x1=32 x2=30

s1=1.5 s2=1.9

A) 4.361 B) 3.287 C) 2.892 D) 1.986

7) Findthestandardizedteststatistic,t,totesttheclaimthatμ1=μ2.Twosamplesarerandomlyselectedand

comefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1=σ 2

n1=14n2=12

x1=5x

2=6

s1=2.5 s2=2.8

A) –0.962 B) –0.813 C) –1.326 D) –1.101

8) Findthestandardizedteststatistic,t,totesttheclaimthatμ1>μ2.Twosamplesarerandomlyselectedand

comefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1≠σ 2

n1=18 n2=13

x1=760 x2=745

s1=40 s2=25

A) 1.282 B) 3.271 C) 2.819 D) 1.865

Page160

9) Findthestandardizedteststatistic,t,totesttheclaimthatμ1<μ2.Twosamplesarerandomlyselectedand

comefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1=σ 2

n1=15n2=15

x1=24.42 x2=26.97

s1=2.9s2=2.8

A) –2.450 B) –3.165 C) –1.667 D) –0.669

10) Findthestandardizedteststatistic,t,totesttheclaimthatμ1≠μ2.Twosamplesarerandomlyselectedand

comefrompopulationsthatarenormal.Thesamplestatisticsaregivenbelow.Assumethat

σ2

1≠σ 2

2.

n1=11n2=18

x1=8.7 x2=9.1

s1=0.76 s2=0.51

A) –1.546 B) –1.821 C) –2.123 D) –1.326

11) Supposeyouwanttotesttheclaimthatμ1=μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Atalevelofsignificanceof

α=0.01,whenshouldyourejectH0?

n1=25n2=30

x1=21 x2=19

s1=1.5 s2=1.9

A) RejectH0ifthestandardizedteststatisticislessthan–2.797orgreaterthan2.797.

B) RejectH0ifthestandardizedteststatisticislessthan–2.789orgreaterthan2.797.

C) RejectH0ifthestandardizedteststatisticislessthan–1.711orgreaterthan1.711.

D) RejectH0ifthestandardizedteststatisticislessthan–2.492orgreaterthan2.492.

12) Supposeyouwanttotesttheclaimthatμ1=μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Atalevelofsignificanceof

α=0.05,whenshouldyourejectH0?

n1=14n2=12

x1=9x2=10

s1=2.5 s2=2.8

A) RejectH0ifthestandardizedteststatisticislessthan–2.064orgreaterthan2.064.

B) RejectH0ifthestandardizedteststatisticislessthan–2.492orgreaterthan2.492

C) RejectH0ifthestandardizedteststatisticislessthan–1.711orgreaterthan1.711.

D) RejectH0ifthestandardizedteststatisticislessthan–1.318orgreaterthan1.318.

Page161

13) Supposeyouwanttotesttheclaimthatμ1>μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Atalevelofsignificanceof

α=0.01,whenshouldyourejectH0?

n1=18 n2=13

x1=425 x2=410

s1=40s2=25

A) RejectH0ifthestandardizedteststatisticisgreaterthan2.681.

B) RejectH0ifthestandardizedteststatisticisgreaterthan1.699.

C) RejectH0ifthestandardizedteststatisticisgreaterthan2.179.

D) RejectH0ifthestandardizedteststatisticisgreaterthan3.055.

14) Supposeyouwanttotesttheclaimthatμ1<μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

2.Atalevelofsignificanceof

α=0.10, whenshouldyourejectH0?

n1=15n2=15

x1=26.17 x2=28.72

s1=2.9s2=2.8

A) RejectH0ifthestandardizedteststatisticislessthan–1.313.

B) RejectH0ifthestandardizedteststatisticislessthan–2.467.

C) RejectH0ifthestandardizedteststatisticislessthan–1.701.

D) RejectH0ifthestandardizedteststatisticislessthan–0.683.

15) Supposeyouwanttotesttheclaimthatμ1≠μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.Assumethatσ2

1≠σ 2

2.Atalevelofsignificanceof

α=0.20,whenshouldyourejectH0?

n1=11n2=18

x1=4.4 x2=4.8

s1=0.76 s2=0.51

A) RejectH0ifthestandardizedteststatisticislessthan–1.372orgreaterthan1.372.

B) RejectH0ifthestandardizedteststatisticislessthan–0.684orgreaterthan0.684.

C) RejectH0ifthestandardizedteststatisticislessthan–2.228orgreaterthan2.228.

D) RejectH0ifthestandardizedteststatisticislessthan–3.169orgreaterthan3.169.

Page162

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

16) Testtheclaimthatμ1=μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesamplestatistics

aregivenbelow.Assumethatσ 2

1≠σ 2

2.Useα=0.05.

n1=25n2=30

x1=33 x2=31

s1=1.5 s2=1.9

17) Testtheclaimthatμ1=μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesamplestatistics

aregivenbelow.Assumethatσ 2

1=σ 2

2.Useα=0.05.

n1=14n2=12

x1=13 x2=14

s1=2.5 s2=2.8

18) Testtheclaimthatμ1>μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesamplestatistics

aregivenbelow.Assumethatσ 2

1≠σ 2

2.Useα=0.01.

n1=18 n2=13

x1=505 x2=490

s1=40s2=25

19) Testtheclaimthatμ1<μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesamplestatistics

aregivenbelow.Assumethatσ 2

1=σ 2

2.Useα=0.025.

n1=15n2=15

x1=22.63 x2=25.18

s1=2.9s2=2.8

20) Testtheclaimthatμ1≠μ2.Twosamplesarerandomlyselectedfromnormalpopulations.Thesamplestatistics

aregivenbelow.Assumethatσ 2

1≠σ 2

2.Useα=0.02.

n1=11n2=18

x1=8.7 x2=9.1

s1=0.76 s2=0.51

Page163

21) Alocalbankclaimsthatthewaitingtimeforitscustomerstobeservedisthelowestinthearea.Acompetitorʹs

bankchecksthewaitingtimesatbothbanks.Thesamplestatisticsarelistedbelow.Testthelocalbankʹsclaim:

(a)assumingthatσ 2

1=σ 2

2,and(b)assumingthatσ2

1≠σ 2

2.Useα=0.05.

LocalBankCompetitorBank

n1=15 n2=16

x1=5.3minutes x2=5.6minutes

s1=1.1minutes s2=1.0minutes

22) Astudywasconductedtodetermineifthesalariesofelementaryschoolteachersfromtwoneighboring

districtswereequal.Asampleof15teachersfromeachdistrictwasrandomlyselected.Themeanfromthefirst

districtwas$28,900withastandarddeviationof$2300.Themeanfromtheseconddistrictwas$30,300witha

standarddeviationof$2100.Testtheclaimthatthesalariesfrombothdistrictsareequal.Assumethat

σ2

1=σ 2

2.Useα=0.05.

23) AsportsanalystclaimsthatthemeanbattingaverageforteamsintheAmericanLeagueisnotequaltothe

meanbattingaverageforteamsintheNationalLeaguebecauseapitcherdoesnotbatintheAmericanLeague.

Thedatalistedbelowarefromrandomlyselectedteamsinbothleagues.Atα

=0.05,testthesportsanalystʹs

claim.Assumethepopulationvariancesareequal.

AmericanLeague NationalLeague

0.279 0.274 0.271 0.268 0.284 0.267 0.266 0.263

0.265 0.254 0.240 0.261 0.259 0.256

24) Awomenʹsadvocacygroupclaimsthatwomengolfersreceivesignificantlylessprizemoneythantheirmale

counterpartswhentheywinfirstplaceinaprofessionaltournament.Thedatalistedbelowarethefirstplace

prizemoniesfromrandomlyselectedmaleandfemaletournamentwinners.Atα

=0.01,testthegroupʹsclaim.

Assumethepopulationvariancesarenotequal.

FemaleGolfers

180,000 150,000 240,000 195,000 202,500

120,000 165,000 225,000 150,000 315,000

MaleGolfers

864,000 810,000 1,170,000 810,000 630,000

1,050,000 945,000 1,008,000 900,000 756,000

630,000 900,000

Page164

3 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

25) Constructa90%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

n1=10n2=12

x1=25x2=23

s1=1.5s2=1.9

A) (0.721,3.279) B) (1.335,3.012) C) (1.413,3.124) D) (1.554,3.651)

26) Constructa95%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

n1=11n2=18

x1=4.8x2=5.2

s1=0.76s2=0.51

A) (–0.883,0.083) B) (–4.152,3.981) C) (–2.762,2.762) D) (–1.762,1.762)

27) Constructa95%confidenceintervalforμ1–μ2.Twosamplesarerandomlyselectedfromnormalpopulations.

Thesamplestatisticsaregivenbelow.Assumethatσ2

1=σ 2

n1=8n2=7

x1=4.1x2=5.5

s1=0.76s2=2.51

A) (–3.406,0.606) B) (–1.132,1.543) C) (–1.679,1.987) D) (2.112,2.113)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

28) AsportsanalystclaimsthatthemeanbattingaverageforteamsintheAmericanLeagueisnotequaltothe

meanbattingaverageforteamsintheNationalLeaguebecauseapitcherdoesnotbatintheAmericanLeague.

Thedatalistedbelowarefromrandomlyselectedteamsinbothleagues.Constructa95%confidenceinterval

forthedifferenceinthemeansμ1–μ2.Assumethepopulationvariancesareequal.

AmericanLeague NationalLeague

0.279 0.274 0.271 0.268 0.284 0.267 0.266 0.263

0.265 0.254 0.240 0.261 0.259 0.256

Page165

29) Awomenʹsadvocacygroupclaimsthatwomengolfersreceivesignificantlylessprizemoneythantheirmale

counterpartswhentheywinfirstplaceinaprofessionaltournament.Thedatalistedbelowarethefirstplace

prizemoniesfromrandomlyselectedmaleandfemaletournamentwinners.Constructa99%confidence

intervalforthedifferenceinthemeansμ1–μ2.Assumethepopulationvariancesarenotequal.

FemaleGolfers

180,000 150,000 240,000 195,000 202,500

120,000 165,000 225,000 150,000 315,000

MaleGolfers

864,000 810,000 1,170,000 810,000 630,000

1,050,000 945,000 1,008,000 900,000 756,000

630,000 900,000

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

30) Astudywasconductedtodetermineifthesalariesofelementaryschoolteachersfromtwoneighboring

districtswereequal.Asampleof15teachersfromeachdistrictwasrandomlyselected.Themeanfromthefirst

districtwas$28,900withastandarddeviationof$2300.Themeanfromtheseconddistrictwas$30,300witha

standarddeviationof$2100.Constructa95%confidenceintervalforμ

1–μ2.Assumethatσ2

1=σ 2

A) (–3047,247) B) (–2054,238) C) (–2871,567) D) (–4081,597)

8.3 TestingtheDifferenceBetweenMeans(DependentSamples)

1 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) DatasetsAandBaredependent.Findd.

A36 34 53 49 37

B34 30 3141 28

A) 9.0 B) –5.1 C) 33.1 D) 25.2

2) DatasetsAandBaredependent.Findd.

A2.1 3.1 5.0 2.0 2.1

B 4.5 3.4 3.3 3.2 4.6

A) –0.94 B) –0.76 C) 0.58 D) 0.89

3) DatasetsAandBaredependent.Findsd.

A40 38 57 53 41

B38 34 3545 32

A) 7.8 B) 5.6 C) 6.8 D) 8.9

Page166

4) DatasetsAandBaredependent.Findsd.

A5.8 6.8 8.7 5.7 5.8

B 8.2 7.1 7.0 6.9 8.3

A) 1.73 B) 1.21 C) 1.32 D) 1.89

5) DatasetsAandBaredependent.Findthecriticalvalue,t0

totesttheclaimthatμd=0.Useα=0.05.

A16 14 33 29 17

B14 10 1121 8

A) ±2.776 B) 2.132 C) ±4.604 D) 3.747

6) DatasetsAandBaredependent.Findthecriticalvalue,t0

totesttheclaimthatμd=0.Useα=0.01.

A5.8 6.8 8.7 5.7 5.8

B 8.2 7.1 7.0 6.9 8.3

A) ±4.604 B) ±3.747 C) 2.132 D) 0.741

7) DatasetsAandBaredependent.Findthecriticalvalue,t0

totesttheclaimthatμd=0.Useα=0.02.

A5.5 6.7 8.6 5.6 5.7

B 2.9 1.8 2.7 1.6 3

A) ±3.747 B) ±4.604 C) 2.132 D) 0.741

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

8) DatasetsAandBaredependent.Testtheclaimthatthepairedsampledataisfromapopulationwithamean

differenceof0.Useα=0.05.

A15 13 32 28 16

B13 9 1020 7

9) DatasetsAandBaredependent.Testtheclaimthatthepairedsampledataisfromapopulationwithamean

differenceof0.Useα=0.01.

A6.8 7.8 9.7 6.7 6.8

B 9.2 8.1 8.0 7.9 9.3

10) Testtheclaimthatμd=0usingthesamplestatisticsbelow.Assumethatthepopulationsarenormally

distributed.Useα=0.05.

Samplestatistics:n=12,d=8.2,sd=1.4

11) Testtheclaimthatμd>0usingthesamplestatisticsbelow.Assumethatthepopulationsarenormally

distributed.Useα=0.01.

Samplestatistics:n=15,d=3.4,sd=0.6

12) Testtheclaimthatμd<0usingthesamplestatisticsbelow.Assumethatthepopulationsarenormally

distributed.Useα=0.10.

Samplestatistics:n=18,d=–3.3,sd=0.4

Page167

13) Testtheclaimthatμd≠0usingthesamplestatisticsbelow.Assumethatthepopulationsarenormally

distributed.Useα=0.02.

Samplestatistics:n=13,d=1.6,sd=5.1

14) NinestudentstooktheSAT.Theirscoresarelistedbelow.Lateron,theytookatestpreparationcourseand

retooktheSAT.Theirnewscoresarelistedbelow.Testtheclaimthatthetestpreparationhadnoeffectontheir

scores.Useα=0.05.Assumethatthedistributionisnormallydistributed.

Student 1234567 8 9

Scoresbeforecourse 720 860 850 880 860 710 850 1200 950

Scoresaftercourse 740 860 840 920 890 720 840 1240 970

15) Aweight–liftingcoachclaimsthatweight–lifterscanincreasetheirstrengthbytakingacertainsupplement.To

testthetheory,thecoachrandomlyselects9athletesandgivesthemastrengthtestusingabenchpress.The

resultsarelistedbelow.Thirtydayslater,afterregulartrainingusingthesupplement,theyaretestedagain.

Thenewresultsarelistedbelow.Testtheclaimthatthesupplementiseffectiveinincreasingtheathletesʹ

strength.Useα=0.05.Assumethatthedistributionisnormallydistributed.

Athlete 123456789

Before 215 240 188 212 275 260 225 200 185

After 225 245 188 210 282 275 230 195 190

16) Apharmaceuticalcompanywishestotestanewdrugwiththeexpectationofloweringcholesterollevels.Ten

subjectsarerandomlyselectedandpretested.Theresultsarelistedbelow.Thesubjectswereplacedonthe

drugforaperiodof6months,afterwhichtheircholesterollevelsweretestedagain.Theresultsarelisted

below.(Allunitsaremilligramsperdeciliter.)Testthecompanyʹsclaimthatthedruglowerscholesterollevels.

Useα=0.01.Assumethatthedistributionisnormallydistributed.

Subject

Before

After

195

180

225

220

202

210

195

175

170

250

235

205

268

250

190

240

225

17) Inastudyofeffectivenessofphysicalexerciseonweightloss,20peoplewererandomlyselectedtoparticipate

inaprogramfor30days.Testtheclaimthatexercisehadnobearingonweightloss.Use

α=0.02.Assumethatthedistributionisnormallydistributed.

WeightbeforeProgram

(inpounds)

Weightafterprogram

(inpounds)

178

182

210

205

156

188

190

193

183

225

220

190

195

165

155

168

165

200

WeightbeforeProgram

(inpounds)Conʹt

Weightafterprogram

(inpounds)Conʹt

186

180

172

173

166

165

184

186

225

240

145

138

208

203

214

203

148

142

174

Page168

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

18) NinestudentstooktheSAT.Theirscoresarelistedbelow.Lateron,theytookatestpreparationcourseand

retooktheSAT.Theirnewscoresarelistedbelow.Constructa95%confidenceintervalforμ

d.Assumethatthe

distributionisnormallydistributed.

Student 1234567 8 9

Scoresbeforecourse 720 860 850 880 860 710 850 1200 950

Scoresaftercourse 740 860 840 920 890 720 840 1240 970

A) (–30.50,–0.62) B) (–20.34,4.85) C) (–10.32,15.44) D) (1.65,30.59)

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

19) Alocalschooldistrictisconcernedaboutthenumberofschooldaysmissedbyitsteachersduetoillness.A

randomsampleof10teachersisselected.Thenumberofdaysabsentinoneyearislistedbelow.Anincentive

programisofferedinanattempttodecreasethenumberofdaysabsent.Thenumberofdaysabsentinoneyear

aftertheincentiveprogramislistedbelow.Testtheclaimthattheincentiveprogramcutsdownonthenumber

ofdaysmissedbyteachers.Useα=0.05.Assumethatthedistributionisnormallydistributed.

Teacher

Daysabsentbefore

incentive

Daysabsentafter

incentive

A

B

C

D

E

F

G

H

I

J

20) Aphysicianclaimsthatapersonʹsdiastolicbloodpressurecanbeloweredif,insteadoftakingadrug,the

personlistenstoarelaxationtapeeachevening.Tensubjectsarerandomlyselectedandpretested.Theirblood

pressures,measuredinmillimetersofmercury,arelistedbelow.The10patientsaregiventhetapesandtoldto

listentothemeacheveningforonemonth.Attheendofthemonth,theirbloodpressuresaretakenagain.The

dataarelistedbelow.Testthephysicianʹsclaim.Useα=0.01.

Patient

Before

After

1

2

3

4

5

6

7

8

9

10

2 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

21) Constructa95%confidenceintervalfordatasetsAandB.DatasetsAandBaredependent.Roundtothe

nearesttenth.

A30 28 47 43 31

B2824253522

A) (–0.7,18.7) B) (–1.3,9.0) C) (–0.1,12.8) D) (–15.3,15.4)

22) Constructa99%confidenceintervalfordatasetsAandB.DatasetsAandBaredependent.Roundtothe

nearesttenth.

A5.8 6.8 8.7 5.7 5.8

B 8.2 7.1 7.0 6.9 8.3

A) (–4.5,2.6) B) (–25.1,5.8) C) (–21.3,19.0) D) (–15.1,15.1)

Page169

8.4 TestingtheDifferenceBetweenProportions

1 TestaClaimAbouttheDifferenceBetweenTwoPopulationProportions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Findtheweightedestimate,ptotesttheclaimthatp1=p2.Useα=0.05.Thesamplestatisticslistedbeloware

fromindependentsamples.

Samplestatistics:n1=50,x1=35,andn2=60,x2=40

A) 0.682 B) 0.328 C) 0.238 D) 1.367

2) Findtheweightedestimate,ptotesttheclaimthatp1>p2.Useα=0.01.Thesamplestatisticslistedbeloware

fromindependentsamples.

Samplestatistics:n1=100,x1=38,andn2=140,x2=50

A) 0.367 B) 0.523 C) 0.179 D) 0.633

3) Findtheweightedestimate,p,totesttheclaimthatp1<p2.Useα=0.10.Thesamplestatisticslistedbeloware

fromindependentsamples.

Samplestatistics:n1=550,x1=121,andn2=690,x2=195

A) 0.255 B) 0.730 C) 0.338 D) 1.116

4) Findtheweightedestimate,ptotesttheclaimthatp1≠p2.Useα=0.02.Thesamplestatisticslistedbeloware

fromindependentsamples.

Samplestatistics:n1=1000,x1=250,andn2=1200,x2=195

A) 0.202 B) 0.789 C) 0.110 D) 0.138

5) Findthestandardizedteststatistic,ztotesttheclaimthatp1=p2.Thesamplestatisticslistedbelowarefrom

independentsamples.

Samplestatistics:n1=50,x1=35,andn2=60,x2=40

A) 0.374 B) 0.982 C) 1.328 D) 2.361

6) Findthestandardizedteststatisticestimate,z,totesttheclaimthatp1>p2.Thesamplestatisticslistedbelow

arefromindependentsamples.

Samplestatistics:n1=100,x1=38,andn2=140,x2=50

A) 0.362 B) 2.116 C) 1.324 D) 0.638

7) Findthestandardizedteststatistic,z,totesttheclaimthatp1<p2.Thesamplestatisticslistedbelowarefrom

independentsamples.

Samplestatistics:n1=550,x1=121,andn2=690,x2=195

A) –2.513 B) –2.132 C) –0.985 D) 1.116

Page170

8) Findthestandardizedteststatistic,z,totesttheclaimthatp1≠p2.Thesamplestatisticslistedbelowarefrom

independentsamples.

Samplestatistics:n1=1000,x1=250,andn2=1200,x2=195

A) 5.09 B) 2.80 C) 4.76 D) 3.21

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

9) Testtheclaimthatp1=p2.Useα=0.05.Thesamplestatisticslistedbelowarefromindependentsamples.

Samplestatistics:n1=50,x1=35,andn2=60,x2=40

10) Testtheclaimthatp1>p2.Useα=0.01.Thesamplestatisticslistedbelowarefromindependentsamples.

Samplestatistics:n1=100,x1=38,andn2=140,x2=50

11) Testtheclaimthatp1<p2.Useα=0.10.Thesamplestatisticslistedbelowarefromindependentsamples.

Samplestatistics:n1=550,x1=121,andn2=690,x2=195

12) Testtheclaimthatp1≠p2.Useα=0.02.Thesamplestatisticslistedbelowarefromindependentsamples.

Samplestatistics:n1=1000,x1=250,andn2=1200,x2=195.

13) Inarecentsurveyofguncontrollaws,arandomsampleof1000womenshowedthat65%wereinfavorof

stricterguncontrollaws.Inarandomsampleof1000men,60%favoredstricterguncontrollaws.Testtheclaim

thatthepercentageofmenandwomenfavoringstricterguncontrollawsisthesame.Use α=0.05.

14) Arecentsurveyshowedthatinasampleof100elementaryschoolteachers,15smoked.Inasampleof180high

schoolteachers,36smoked.Istheproportionofhighschoolteacherswhosmokegreaterthantheproportionof

elementaryteacherswhosmoke?Useα=0.01.

15) Inasurveyof500doctorsthatpracticespecializedmedicine,20%feltthatthegovernmentshouldcontrol

healthcare.Inasampleof800doctorsthatweregeneralpractitioners,30%feltthatthegovernmentshould

controlhealthcare.Testtheclaimthatthereisadifferenceintheproportions.Useα

=0.10.

16) AnutritionistbelievesthatobesityismoreprevalentamongAmericanadultsthanitwasinthepast.He

discoversthatinastudyconductedintheyear1994,380ofthe1630randomlychosenadultswereclassifiedas

obese.However,inamorerecentstudy,hefinds726outof2350randomlychosenadultswereclassifiedas

obese.Atα=0.05,dothesestudiesprovideevidencetosupportthenutritionistʹsclaimthattheproportionof

obeseadultshassignificantlyincreasedsince1994?

17) Totesttheeffectivenessofanewdrugdesignedtorelievepain,200patientswererandomlyselectedand

dividedintotwoequalgroups.Onegroupof100patientswasgivenapillcontainingthedrugwhiletheother

groupof100wasgivenaplacebo.Whatcanweconcludeabouttheeffectivenessofthedrugif62ofthose

actuallytakingthedrugfeltabeneficialeffectwhile41ofthepatientstakingtheplacebofeltabeneficialeffect?

Useα=0.05.

18) Arandomsampleof100studentsatahighschoolwasaskedwhethertheywouldasktheirfatherormotherfor

helpwithahomeworkassignmentinscience.Asecondsampleof100differentstudentswasaskedthesame

questionforanassignmentinhistory.If43studentsinthefirstsampleand47studentsinthesecondsample

repliedthattheyturnedtotheirmotherratherthantheirfatherforhelp,testtheclaimwhetherthedifference

betweentheproportionsisduetochance.Useα=0.02.

Page171

19) IntheinitialtestoftheSalkvaccineforpolio,400,000childrenwereselectedanddividedintotwogroupsof

200,000.OnegroupwasvaccinatedwiththeSalkvaccinewhilethesecondgroupwasvaccinatedwitha

placebo.OfthosevaccinatedwiththeSalkvaccine,33laterdevelopedpolio.Ofthosereceivingtheplacebo,115

laterdevelopedpolio.TesttheclaimthattheSalkvaccineiseffectiveinloweringthepoliorate.Useα

=0.01.

20) Awell–knownstudyof22,000malephysicianswasconductedtodetermineiftakingaspirindailyreducesthe

chancesofaheartattack.Halfofthephysiciansweregivenaregulardoseofaspirinwhiletheotherhalfwas

givenplacebos.Sixyearslater,amongthosewhotookaspirin,104sufferedheartattackswhileamongthose

whotookplacebos,189sufferedheartattacks.Doesitappearthattheaspirincanreducethenumberofheart

attacksamongthesamplegroupthattookaspirin?Useα

=0.01.

21) Ayouthpreventionorganizationisexaminingtheeffectofparentalsmokingonthedecisionoftheirteenagers

tosmoke.Asurveyof1150teenagers,ages11to17yearswhosmokedinthelast30days,wasconducted.The

randomsampleconsistedof500teenagerswhohadatleastoneparentthatsmokedand650whohadparents

thatdidnotsmoke.Theresultsareshowninthefigure.Atα

=0.01,canyousupporttheorganizationʹsclaim

thattheproportionofteenswhodecidetosmokeisgreaterwhenoneorbothoftheirparentssmoke?

Page172

22) Ayouthpreventionorganizationisexaminingtheeffectofpeerpressureonthedecisionofteenagerstosmoke.

Asurveyof97teenagers,ages11to17yearswhosmokedinthelast30days,wasconducted.Therandom

sampleconsistedof25teenagerswhosaidall/mostoftheirfriendssmoke,40whosaidsomeoftheirfriends

smoke,and32whosaidnoneoftheirfriendssmoke.Theresultsareshowninthefigure.Atα

=0.01,canyou

supporttheorganizationʹsclaimthattheproportionofteenswhodecidetosmokeislowerwhennoneoftheir

friendssmoke?

2 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationProportions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

23) Constructa95%confidenceintervalforp1–p2.Thesamplestatisticslistedbelowarefromindependent

samples.

Samplestatistics:n1=50,x1=35,andn2=60,x2=40

A) (–0.141,0.208) B) (–0.871,0.872) C) (–1.341,1.781) D) (–2.391,3.112)

24) Constructa98%confidenceintervalforp1–p2.Thesamplestatisticslistedbelowarefromindependent

samples.

Samplestatistics:n1=1000,x1=250,andn2=1200,x2=195

A) (0.047,0.128) B) (–0.621,0.781) C) (0.581,1.819) D) (1.516,3.021)

25) Inarecentsurveyofguncontrollaws,arandomsampleof1000womenshowedthat65%wereinfavorof

stricterguncontrollaws.Inarandomsampleof1000men,60%favoredstricterguncontrollaws.Constructa

95%confidenceintervalforp1p2.

A) (0.008,0.092) B) (0.587,0.912) C) (–1.423,1.432) D) (–2.153,1.679)

26) Constructa95%confidenceintervalforp1–p2forasurveythatfinds30%of240malesand41%of200

femalesareopposedtothedeathpenalty.

A) (–0.200,–0.021) B) (–1.532,1.342) C) (–0.561,0.651) D) (–1.324,1.512)

Page173

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

27) AnutritionistbelievesthatobesityismoreprevalentamongAmericanadultsthanitwasinthepast.He

discoversthatinastudyconductedintheyear1994,380ofthe1630randomlychosenadultswereclassifiedas

obese.However,inamorerecentstudy,hefinds726outof2350randomlychosenadultswereclassifiedas

obese.Constructa95%confidenceintervalforthedifferenceinproportionsp1–p2.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

28) Arandomsampleof100studentsatahighschoolwasaskedwhethertheywouldasktheirfatherormotherfor

helpwithahomeworkassignmentinscience.Asecondsampleof100differentstudentswasaskedthesame

questionforanassignmentinhistory.Forty–threestudentsinthefirstsampleand47studentsinthesecond

samplerepliedthattheyturnedtotheirmotherratherthantheirfatherforhelp.Constructa98%confidence

intervalforp1–p2.

A) (–0.204,0.124) B) (–1.324,1.521) C) (–0.591,0.762) D) (–1.113,1.311)

Page174

Ch.8 HypothesisTestingwithTwoSamples

AnswerKey

8.1 TestingtheDifferenceBetweenMeans(LargeIndependentSamples)

1 DeterminetheDifferenceBetweenDependentandIndependentSamples

2 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

Page175

3 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

8.2 TestingtheDifferenceBetweenMeans(SmallIndependentSamples)

1 FindCriticalValues

2 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

3 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

Page176

8.3 TestingtheDifferenceBetweenMeans(DependentSamples)

1 TestaClaimAbouttheDifferenceBetweenTwoPopulationMeans

2 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationMeans

8.4 TestingtheDifferenceBetweenProportions

1 TestaClaimAbouttheDifferenceBetweenTwoPopulationProportions

Page177

2 ConstructaConfidenceIntervalfortheDifferenceBetweenTwoPopulationProportions

Page178