Ch.7 HypothesisTestingwithOneSample
7.1 IntroductiontoHypothesisTestin
g
1 StateaNullandAlternativeHypothesis
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) ThemeanageofbusdriversinChicagois48.5 years.Writethenullandalternativehypotheses.
2) ThemeanIQofstatisticsteachersisgreaterthan110.Writethenullandalternativehypotheses.
3) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan101 pointspergame.Writethenull
andalternativehypotheses.
4) Acandidateforgovernorofaparticularstateclaimstobefavoredbyatleasthalfofthevoters.Writethenull
andalternativehypotheses.
5) ThedeanofamajoruniversityclaimsthatthemeantimeforstudentstoearnaMasterʹsdegreeisatmost4.9
years.Writethenullandalternativehypotheses.
6) Thebuyerofalocalhikingclubstorerecommendsagainstbuyingthenewdigitalaltimetersbecausetheyvary
morethantheoldaltimeters,whichhadastandarddeviationofoneyard.Writethenullandalternative
hypotheses.
7) ThemeanageofbusdriversinChicagois53.7 years.Statethisclaimmathematically.Writethenulland
alternativehypotheses.Identifywhichhypothesisistheclaim.
8) ThemeanIQofstatisticsteachersisgreaterthan120.Statethisclaimmathematically.Writethenulland
alternativehypotheses.Identifywhichhypothesisistheclaim.
9) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan101 pointspergame.Statethis
claimmathematically.Writethenullandalternativehypotheses.Identifywhichhypothesisistheclaim.
10) Acandidateforgovernorofaparticularstateclaimstobefavoredbyatleasthalfofthevoters.Statethisclaim
mathematically.Writethenullandalternativehypotheses.Identifywhichhypothesisistheclaim.
11) ThedeanofamajoruniversityclaimsthatthemeantimeforstudentstoearnaMasterʹsdegreeisatmost3.3
years.Statethisclaimmathematically.Writethenullandalternativehypotheses.Identifywhichhypothesisis
theclaim.
12) Thebuyerofalocalhikingclubstorerecommendsagainstbuyingthenewdigitalaltimetersbecausetheyvary
morethantheoldaltimeters,whichhadastandarddeviationofoneyard.Statethisclaimmathematically.
Writethenullandalternativehypotheses.Identifywhichhypothesisistheclaim.
2 IdentifyWhethertoUseaOne–tailedorTwo–tailedTest
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
13) GivenH0:p≥80%andHa:p<80%,determinewhetherthehypothesistestisleft–tailed,right–tailed,or
two–tailed.
A) left–tailed B) right–tailed C) two–tailed
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14) GivenH0:μ≤25andHa:μ>25,determinewhetherthehypothesistestisleft–tailed,right–tailed,or
two–tailed.
A) right–tailed B) left–tailed C) two–tailed
15) Aresearcherclaimsthat62%ofvotersfavorguncontrol.Determinewhetherthehypothesistestforthisclaim
isleft–tailed,right–tailed,ortwo–tailed.
A) two–tailed B) left–tailed C) right–tailed
16) Abreweryclaimsthatthemeanamountofbeerintheirbottlesisatleast12ounces.Determinewhetherthe
hypothesistestforthisclaimisleft–tailed,right–tailed,ortwo–tailed.
A) left–tailed B) right–tailed C) two–tailed
17) Acarmakerclaimsthatitsnewsub–compactcargetsbetterthan47 milespergallononthehighway.
Determinewhetherthehypothesistestforthisisleft–tailed,right–tailed,ortwo–tailed.
A) right–tailed B) left–tailed C) two–tailed
18) Theownerofaprofessionalbasketballteamclaimsthatthemeanattendanceatgamesisover30,000 and
thereforetheteamneedsanewarena.Determinewhetherthehypothesistestforthisclaimisleft–tailed,
right–tailed,ortwo–tailed.
A) right–tailed B) left–tailed C) two–tailed
19) Anelementaryschoolclaimsthatthestandarddeviationinreadingscoresofitsfourthgradestudentsisless
than4.35.Determinewhetherthehypothesistestforthisclaimisleft–tailed,right–tailed,ortwo–tailed.
A) left–tailed B) right–tailed C) two–tailed
3 IdentifyTypeIandTypeIIErrors
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
20) ThemeanageofbusdriversinChicagois52.5 years.IdentifythetypeIandtypeIIerrorsforthehypothesis
testofthisclaim.
21) ThemeanIQofstatisticsteachersisgreaterthan120.IdentifythetypeIandtypeIIerrorsforthehypothesis
testofthisclaim.
22) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan105 pointspergame.Identifythe
typeIandtypeIIerrorsforthehypothesistestofthisclaim.
23) Acandidateforgovernorofacertainstateclaimstobefavoredbyatleasthalfofthevoters.IdentifythetypeI
andtypeIIerrorsforthehypothesistestofthisclaim.
4 InterpretaDecisionBasedontheResultsofaStatisticalTest
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
24) ThemeanageofbusdriversinChicagois50.2 years.Ifahypothesistestisperformed,howshouldyou
interpretadecisionthatrejectsthenullhypothesis?
A) Thereissufficientevidencetorejecttheclaimμ =50.2.
B) Thereisnotsufficientevidencetorejecttheclaimμ =50.2.
C) Thereissufficientevidencetosupporttheclaimμ=50.2.
D) Thereisnotsufficientevidencetosupporttheclaimμ =50.2.
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25) ThemeanageofbusdriversinChicagois59.3 years.Ifahypothesistestisperformed,howshouldyou
interpretadecisionthatfailstorejectthenullhypothesis?
A) Thereisnotsufficientevidencetorejecttheclaimμ =59.3.
B) Thereissufficientevidencetorejecttheclaimμ =59.3.
C) Thereissufficientevidencetosupporttheclaimμ=59.3.
D) Thereisnotsufficientevidencetosupporttheclaimμ =59.3.
26) ThemeanageofbusdriversinChicagoisgreaterthan57.8 years.Ifahypothesistestisperformed,howshould
youinterpretadecisionthatrejectsthenullhypothesis?
A) Thereissufficientevidencetosupporttheclaimμ>57.8.
B) Thereissufficientevidencetorejecttheclaimμ >57.8.
C) Thereisnotsufficientevidencetorejecttheclaimμ >57.8.
D) Thereisnotsufficientevidencetosupporttheclaimμ >57.8.
27) ThemeanageofbusdriversinChicagoisgreaterthan47.6 years.Ifahypothesistestisperformed,howshould
youinterpretadecisionthatfailstorejectthenullhypothesis?
A) Thereisnotsufficientevidencetosupporttheclaimμ >47.6.
B) Thereissufficientevidencetorejecttheclaimμ >47.6.
C) Thereisnotsufficientevidencetorejecttheclaimμ >47.6.
D) Thereissufficientevidencetosupporttheclaimμ>47.6.
28) ThemeanIQofstatisticsteachersisgreaterthan160.Ifahypothesistestisperformed,howshouldyou
interpretadecisionthatrejectsthenullhypothesis?
A) Thereissufficientevidencetosupporttheclaimμ>160.
B) Thereissufficientevidencetorejecttheclaimμ >160.
C) Thereisnotsufficientevidencetorejecttheclaimμ >160.
D) Thereisnotsufficientevidencetosupporttheclaimμ >160.
29) ThemeanIQofstatisticsteachersisgreaterthan150.Ifahypothesistestisperformed,howshouldyou
interpretadecisionthatfailstorejectthenullhypothesis?
A) Thereisnotsufficientevidencetosupporttheclaimμ >150.
B) Thereissufficientevidencetorejecttheclaimμ >150.
C) Thereisnotsufficientevidencetorejecttheclaimμ >150.
D) Thereissufficientevidencetosupporttheclaimμ>150.
30) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan92 pointspergame.Ifahypothesis
testisperformed,howshouldyouinterpretadecisionthatrejectsthenullhypothesis?
A) Thereissufficientevidencetosupporttheclaimμ<92.
B) Thereissufficientevidencetorejecttheclaimμ <92.
C) Thereisnotsufficientevidencetorejecttheclaimμ <92.
D) Thereisnotsufficientevidencetosupporttheclaimμ <92.
31) ThemeanscoreforallNBAgamesduringaparticularseasonwaslessthan100 pointspergame.Ifa
hypothesistestisperformed,howshouldyouinterpretadecisionthatfailstorejectthenullhypothesis?
A) Thereisnotsufficientevidencetosupporttheclaimμ <100.
B) Thereissufficientevidencetorejecttheclaimμ <100.
C) Thereisnotsufficientevidencetorejecttheclaimμ <100.
D) Thereissufficientevidencetosupporttheclaimμ<100.
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32) Acandidateforgovernorofacertainstateclaimstobefavoredbyatleasthalfofthevoters.Ifahypothesistest
isperformed,howshouldyouinterpretadecisionthatrejectsthenullhypothesis?
A) Thereissufficientevidencetorejecttheclaimρ ≥0.5.
B) Thereisnotsufficientevidencetorejecttheclaimρ ≥0.5.
C) Thereissufficientevidencetosupporttheclaimρ ≥0.5.
D) Thereisnotsufficientevidencetosupporttheclaimρ ≥0.5.
33) Acandidateforgovernorofacertainstateclaimstobefavoredbyatleasthalfofthevoters.Ifahypothesistest
isperformed,howshouldyouinterpretadecisionthatfailstorejectthenullhypothesis?
A) Thereisnotsufficientevidencetorejecttheclaimρ ≥0.5.
B) Thereissufficientevidencetorejecttheclaimρ ≥0.5.
C) Thereissufficientevidencetosupporttheclaimρ ≥0.5.
D) Thereisnotsufficientevidencetosupporttheclaimρ ≥0.5.
34) ThedeanofamajoruniversityclaimsthatthemeantimeforstudentstoearnaMasterʹsdegreeisatmost5.8
years.Ifahypothesistestisperformed,howshouldyouinterpretadecisionthatrejectsthenullhypothesis?
A) Thereissufficientevidencetorejecttheclaimμ ≤5.8.
B) Thereisnotsufficientevidencetorejecttheclaimμ ≤5.8.
C) Thereissufficientevidencetosupporttheclaimμ≤5.8.
D) Thereisnotsufficientevidencetosupporttheclaimμ ≤5.8.
35) ThedeanofamajoruniversityclaimsthatthemeantimeforstudentstoearnaMasterʹsdegreeisatmost5.1
years.Ifahypothesistestisperformed,howshouldyouinterpretadecisionthatfailstorejectthenull
hypothesis?
A) Thereisnotsufficientevidencetorejecttheclaimμ ≤5.1.
B) Thereissufficientevidencetorejecttheclaimμ ≤5.1.
C) Thereissufficientevidencetosupporttheclaimμ≤5.1.
D) Thereisnotsufficientevidencetosupporttheclaimμ ≤5.1.
5 UseConfidenceIntervalstoMakeDecisions
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
36) GivenH0:μ≤12,forwhichconfidenceintervalshouldyourejectH0?
A) (13,16) B) (11.5,12.5) C) (10,13)
37) GivenH0:p≥0.45,forwhichconfidenceintervalshouldyourejectH0?
A) (0.32,0.40) B) (0.40,0.50) C) (0.42,0.47)
6 Concepts
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
38) GivenH0:p=0.85andα=0.10,whichlevelofconfidenceshouldyouusetotesttheclaim?
A) 90% B) 95% C) 99% D) 80%
39) GivenH0:μ≥23.5andα=0.05,whichlevelofconfidenceshouldyouusetotesttheclaim?
A) 90% B) 99% C) 80% D) 95%
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7.2 HypothesisTestingfortheMean(LargeSamples)
1 FindP–values
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Supposeyouareusingα=0.05totesttheclaimthatμ>14 usingaP–value.Youaregiventhesamplestatistics
n=50,x=14.3,ands=1.2.FindtheP–value.
A) 0.0384 B) 0.1321 C) 0.0128 D) 0.0012
2) Supposeyouareusingα=0.05totesttheclaimthatμ≠14 usingaP–value.Youaregiventhesamplestatistics
n=35,x=13.1,ands=2.7.FindtheP–value.
A) 0.0488 B) 0.0591 C) 0.1003 D) 0.0244
3) Supposeyouareusingα=0.01totesttheclaimthatμ≤32 usingaP–value.Youaregiventhesamplestatistics
n=40,x=33.8,ands=4.3.FindtheP–value.
A) 0.0040 B) 0.9960 C) 0.0211 D) 0.1030
4) Supposeyouareusingα=0.01totesttheclaimthatμ=1620 usingaP–value.Youaregiventhesample
statisticsn=35,x=1590,ands=82.FindtheP–value.
A) 0.0308 B) 0.0154 C) 0.3169 D) 0.0077
2 TestaClaimAboutaMeanUsingP–values
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
5) GivenH0:μ=25,Ha:μ ≠25,andP=0.034.DoyourejectorfailtorejectH0atthe0.01levelofsignificance?
A) failtorejectH0
B) rejectH0
C) notsufficientinformationtodecide
6) GivenH0:μ≥18andP=0.070.DoyourejectorfailtorejectH0atthe0.05levelofsignificance?
A) failtorejectH0
B) rejectH0
C) notsufficientinformationtodecide
7) GivenHa:μ>85andP=0.007.DoyourejectorfailtorejectH0atthe0.01levelofsignificance?
A) rejectH0
B) failtorejectH0
C) notsufficientinformationtodecide
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
8) Afastfoodoutletclaimsthatthemeanwaitingtimeinlineislessthan3.4 minutes.Arandomsampleof60
customershasameanof3.3minuteswithastandarddeviationof0.6minute.Ifα=0.05,testthefastfood
outletʹsclaim.
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9) Alocalschooldistrictclaimsthatthenumberofschooldaysmissedbyitsteachersduetoillnessisbelowthe
nationalaverageof5.Arandomsampleof40teachersprovidedthedatabelow.Atα
=0.05,testthedistrictʹs
claimusingP–values.
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3 FindCriticalValues
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
10) Findthecriticalvalueforaright–tailedtestwithα =0.01andn=75.
A) 2.33 B) 2.575 C) 1.645 D) 1.96
11) Findthecriticalvalueforatwo–tailedtestwithα =0.01andn=30.
A) ±2.575 B) ±2.33 C) ±1.645 D) ±1.96
12) Findthecriticalvalueforaleft–tailedtestwithα =0.05andn=48.
A) –1.645 B) –2.33 C) –2.575 D) –1.96
13) Findthecriticalvalueforatwo–tailedtestwithα =0.10andn=100.
A) ±1.645 B) ±2.33 C) ±2.575 D) ±1.96
14) Findthecriticalvalueforaleft–tailedtestwithα =0.025andn=50.
A) –1.96 B) –2.33 C) –2.575 D) –1.645
15) Findthecriticalvalueforatwo–tailedtestwithα =0.07 andn=36.
A) ±1.81 B) ±2.33 C) ±2.575 D) ±1.96
4 TestaClaimAboutaMean
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
16) Youwishtotesttheclaimthatμ>32atalevelofsignificanceofα =0.05andaregivensamplestatisticsn=50,
x=32.3,ands=1.2.Computethevalueofthestandardizedteststatistic.Roundyouranswertotwodecimal
places.
A) 1.77 B) 2.31 C) 0.98 D) 3.11
17) Youwishtotesttheclaimthatμ≠22atalevelofsignificanceofα =0.05andaregivensamplestatisticsn=35,
x=21.1,ands=2.7.Computethevalueofthestandardizedteststatistic.Roundyouranswertotwodecimal
places.
A) –1.97 B) –3.12 C) –2.86 D) –1.83
18) Youwishtotesttheclaimthatμ≤38atalevelofsignificanceofα =0.01andaregivensamplestatisticsn=40,
x=39.8,ands=4.3.Computethevalueofthestandardizedteststatistic.Roundyouranswertotwodecimal
places.
A) 2.65 B) 3.51 C) 2.12 D) 1.96
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19) Youwishtotesttheclaimthatμ=1240 atalevelofsignificanceofα =0.01andaregivensamplestatistics
n=35,x=1210ands=82.Computethevalueofthestandardizedteststatistic.Roundyouranswertotwo
decimalplaces.
A) –2.16 B) –3.82 C) –4.67 D) –5.18
20) Supposeyouwanttotesttheclaimthatμ≠3.5.Givenasamplesizeofn=47 andalevelofsignificanceof
α=0.10,whenshouldyourejectH0?
A) RejectH0ifthestandardizedteststatisticisgreaterthan1.645 orlessthan–1.645.
B) RejectH0ifthestandardizedteststatisticisgreaterthan2.575 orlessthan–2.575.
C) RejectH0ifthestandardizedteststatisticisgreaterthan2.33 orlessthan–2.33
D) RejectH0ifthestandardizedteststatisticisgreaterthan1.96 orlessthan–1.96
21) Supposeyouwanttotesttheclaimthatμ≤25.6.Givenasamplesizeofn=53 andalevelofsignificanceof
α=0.01,whenshouldyourejectH0?
A) RejectH0ifthestandardizedteststatisticisgreaterthan2.33.
B) RejectH0ifthestandardizedteststatisticisgreaterthan1.96.
C) RejectH0ifthestandardizedteststatisticisgreaterthan1.645.
D) RejectH0ifthestandardizedteststatisticisgreaterthan2.575.
22) Supposeyouwanttotesttheclaimthatμ≥65.4.Givenasamplesizeofn=35andalevelofsignificanceof
α=0.05,whenshouldyourejectH0?
A) RejectH0ifthestandardizedteststatisticislessthan–1.645.
B) RejectH0ifthestandardizedtestislessthan–1.96.
C) RejectH0ifthestandardizedteststatisticislessthan–2.575.
D) RejectH0ifthestandardizedteststatisticislessthan–1.28.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
23) Testtheclaimthatμ>19,giventhatα=0.05andthesamplestatisticsaren=50,x=19.3,ands=1.2.
24) Testtheclaimthatμ≠38,giventhatα=0.05andthesamplestatisticsaren=35,x=37.1ands=2.7.
25) Testtheclaimthatμ≤22,giventhatα=0.01andthesamplestatisticsaren=40,x=23.8,ands=4.3.
26) Testtheclaimthatμ=1210,giventhatα=0.01andthesamplestatisticsaren=35,x=1180,ands=82.
27) Alocalbrewerydistributesbeerinbottleslabeled12 ounces.Agovernmentagencythinksthatthebreweryis
cheatingitscustomers.Theagencyselects50ofthesebottles,measurestheircontents,andobtainsasample
meanof11.7ounceswithastandarddeviationof0.70ounce.Usea0.01significanceleveltotesttheagencyʹs
claimthatthebreweryischeatingitscustomers.
28) Amanufacturerclaimsthatthemeanlifetimeofitsfluorescentbulbsis1000 hours.Ahomeownerselects40
bulbsandfindsthemeanlifetimetobe980hourswithastandarddeviationof80hours.Testthe
manufacturerʹsclaim.Useα=0.05.
29) Atruckingfirmsuspectsthatthemeanlifetimeofacertaintireitusesislessthan34,000miles.Tocheckthe
claim,thefirmrandomlyselectsandtests54ofthesetiresandgetsameanlifetimeof33,390mileswitha
standarddeviationof1200miles.Atα=0.05,testthetruckingfirmʹsclaim.
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30) Alocalpolitician,runningforreelection,claimsthatthemeanprisontimeforcarthievesislessthanthe
required4years.Asampleof80convictedcarthieveswasrandomlyselected,andthemeanlengthofprison
timewasfoundtobe3yearsand6months,withastandarddeviationof1yearand3months.Atα=0.05,test
thepoliticianʹsclaim.
31) Alocalgroupclaimsthatthepoliceissueatleast60speedingticketsadayintheirarea.Toprovetheirpoint,
theyrandomlyselectonemonth.Theirresearchyieldsthenumberofticketsissuedforeachday.Thedataare
listedbelow.Atα=0.01,testthegroupʹsclaim.
70484168695570576083
32607258884859605665
66606842575949707563
44
32) Afastfoodoutletclaimsthatthemeanwaitingtimeinlineislessthan3.5minutes.Arandomsampleof60
customershasameanof3.6minuteswithastandarddeviationof0.6minute.Ifα
=0.05,testthefastfood
outletʹsclaimusingcriticalvaluesandrejectionregions.
33) Afastfoodoutletclaimsthatthemeanwaitingtimeinlineislessthan3.5minutes.Arandomsampleof60
customershasameanof3.6minuteswithastandarddeviationof0.6minute.Ifα
=0.05,testthefastfood
outletʹsclaimusingconfidenceintervals.
34) Alocalschooldistrictclaimsthatthenumberofschooldaysmissedbyteachersduetoillnessisbelowthe
nationalaverageof5days.Arandomsampleof40teachersprovidedthedatabelow.Atα
=0.05,testthe
districtʹsclaimusingcriticalvaluesandrejectionregions.
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35) Alocalschooldistrictclaimsthatthenumberofschooldaysmissedbyteachersduetoillnessisbelowthe
nationalaverageof5.Arandomsampleof40teachersprovidedthedatabelow.Atα
=0.05,testthedistrictʹs
claimusingconfidenceintervals.
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7.3 HypothesisTestingfortheMean(SmallSamples)
1 FindCriticalValuesinat–distribution
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Findthecriticalvaluesforasamplewithn=15 andα =0.05 ifH0:μ ≤20.
A) 1.761 B) 2.977 C) 2.625 D) 1.345
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2 TestaClaimAboutaMean
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
2) Findthestandardizedteststatistictforasamplewithn=12,x=22.2,s=2.2,andα=0.01ifH0:μ=21.Round
youranswertothreedecimalplaces.
A) 1.890 B) 1.991 C) 2.132 D) 2.001
3) Findthestandardizedteststatistictforasamplewithn=10,x=9.7,s=1.3,andα=0.05ifH0:μ≥10.6.Round
youranswertothreedecimalplaces.
A) –2.189 B) –3.186 C) –3.010 D) –2.617
4) Findthestandardizedteststatistictforasamplewithn=15,x=7.4,s=0.8,andα=0.05ifH0:μ≤7.1.Round
youranswertothreedecimalplaces.
A) 1.452 B) 1.728 C) 1.631 D) 1.312
5) Findthestandardizedteststatistictforasamplewithn=20,x=13,s=2.0,andα=0.05ifHa:μ<13.4.Round
youranswertothreedecimalplaces.
A) –0.894 B) –0.872 C) –1.265 D) –1.233
6) Findthestandardizedteststatistictforasamplewithn=25,x=36,s=3,andα=0.005ifHa:μ>35.Round
youranswertothreedecimalplaces.
A) 1.667 B) 1.997 C) 1.452 D) 1.239
7) Findthestandardizedteststatistictforasamplewithn=12,x=18.8,s=2.1,andα=0.01ifHa:μ≠19.3.
Roundyouranswertothreedecimalplaces.
A) –0.825 B) –0.008 C) –0.037 D) –0.381
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
8) Useat–testtotesttheclaimμ=16atα=0.01,giventhesamplestatisticsn=12,x=17.2,ands=2.2.
9) Useat–testtotesttheclaimμ≥10.2atα=0.05,giventhesamplestatisticsn=10,x=9.3,ands=1.3.
10) Useat–testtotesttheclaimμ≤8.8atα=0.05,giventhesamplestatisticsn=15,x=9.1,ands=0.8.
11) Useat–testtotesttheclaimμ<11atα=0.10,giventhesamplestatisticsn=20,x=10.6,ands=2.0.
12) Useat–testtotesttheclaimμ>39atα=0.005,giventhesamplestatisticsn=25,x=40,ands=3.
13) Useat–testtotesttheclaimμ=23.3atα=0.01,giventhesamplestatisticsn=12,x=22.8,ands=2.1.
14) TheMetropolitanBusCompanyclaimsthatthemeanwaitingtimeforabusduringrushhourislessthan10
minutes.Arandomsampleof20waitingtimeshasameanof8.6minuteswithastandarddeviationof2.1
minutes.Atα=0.01,testthebuscompanyʹsclaim.Assumethedistributionisnormallydistributed.
15) Alocalbrewerydistributesbeerinbottleslabeled12ounces.Agovernmentagencythinksthatthebreweryis
cheatingitscustomers.Theagencyselects20ofthesebottles,measurestheircontents,andobtainsasample
meanof11.7ounceswithastandarddeviationof0.7ounce.Usea0.01significanceleveltotesttheagencyʹs
claimthatthebreweryischeatingitscustomers.
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16) Alocalgroupclaimsthatthepoliceissuemorethan60speedingticketsadayintheirarea.Toprovetheir
point,theyrandomlyselecttwoweeks.Theirresearchyieldsthenumberofticketsissuedforeachday.The
dataarelistedbelow.Atα=0.01,testthegroupʹsclaim.
70 48 41 68 69 55 70
57 60 83 32 60 72 58
17) Alocalgroupclaimsthatthepoliceissuemorethan60speedingticketsadayintheirarea.Toprovetheir
point,theyrandomlyselecttwoweeks.Theirresearchyieldsthenumberofticketsissuedforeachday.The
dataarelistedbelow.Atα=0.02,testthegroupʹsclaimusingconfidenceintervals.
70 48 41 68 69 55 70
57 60 83 32 60 72 58
18) Amanufacturerclaimsthatthemeanlifetimeofitsfluorescentbulbsis1100 hours.Ahomeownerselects25
bulbsandfindsthemeanlifetimetobe1070hourswithastandarddeviationof80hours.Testthe
manufacturerʹsclaim.Useα=0.05.
19) Amanufacturerclaimsthatthemeanlifetimeofitsfluorescentbulbsis1000hours.Ahomeownerselects25
bulbsandfindsthemeanlifetimetobe980hourswithastandarddeviationof80hours.Ifα
=0.05,testthe
manufacturerʹsclaimusingconfidenceintervals.
20) Atruckingfirmsuspectsthatthemeanlifeofacertaintireitusesislessthan35,000miles.Tochecktheclaim,
thefirmrandomlyselectsandtests18ofthesetiresandgetsameanlifetimeof34,400mileswithastandard
deviationof1200miles.Atα=0.05,testthetruckingfirmʹsclaim.
3 TestaClaimAboutaMeanUsingaP–value
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
21) Alocalgroupclaimsthatthepoliceissuemorethan60speedingticketsadayintheirarea.Toprovetheir
point,theyrandomlyselecttwoweeks.Theirresearchyieldsthenumberofticketsissuedforeachday.The
dataarelistedbelow.Atα=0.01,testthegroupʹsclaimusingP–values.
70 48 41 68 69 55 70
57 60 83 32 60 72 58
22) Amanufacturerclaimsthatthemeanlifetimeofitsfluorescentbulbsis1000hours.Ahomeownerselects25
bulbsandfindsthemeanlifetimetobe980hourswithastandarddeviationof80hours.Ifα
=0.05,testthe
manufacturerʹsclaimusingP–values.
23) Afastfoodoutletclaimsthatthemeanwaitingtimeinlineislessthan3.3 minutes.Arandomsampleof20
customershasameanof3.1minuteswithastandarddeviationof0.8minute.Ifα=0.05,testthefastfood
outletʹsclaimusingP–values.
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24) Alocalschooldistrictclaimsthatthenumberofschooldaysmissedbyitsteachersduetoillnessisbelowthe
nationalaverageofμ=5.Arandomsampleof28teachersprovidedthedatabelow.Atα
=0.05,testthe
districtʹsclaimusingP–values.
0363354135
7312332416
25283125
7.4 HypothesisTestingforProportions
1 TestaClaimAboutaProportion
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Determinewhetherthenormalsamplingdistributioncanbeused.Theclaimisp<0.25andthesamplesizeis
n=18.
A) Donotusethenormaldistribution. B) Usethenormaldistribution.
2) Determinewhetherthenormalsamplingdistributioncanbeused.Theclaimisp≥0.325andthesamplesizeis
n=42.
A) Usethenormaldistribution. B) Donotusethenormaldistribution.
3) Determinethecriticalvalue,z0
,
totesttheclaimaboutthepopulationproportionp=0.250givenn=48
andp
^=0.231.Useα=0.01.
A) ±2.575 B) ±1.96 C) ±1.645 D) ±2.33
4) Determinethestandardizedteststatistic,z,totesttheclaimaboutthepopulationproportionp=0.250 given
n=48andp
^=0.231.Useα=0.01.
A) –0.304 B) –1.18 C) –0.23 D) –2.87
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
5) Testtheclaimaboutthepopulationproportionp≠0.325givenn=42andp
^
=0.247.Useα=0.05.
6) Fifty–fivepercentofregisteredvotersinacongressionaldistrictareregisteredDemocrats.TheRepublican
candidatetakesapolltoassesshischancesinatwo–candidaterace.Hepolls1200potentialvotersandfinds
that621plantovotefortheRepublicancandidate.DoestheRepublicancandidatehaveachancetowin?Use
α=0.05.
7) Anairlineclaimsthattheno–showrateforpassengersislessthan5%.Inasampleof420randomlyselected
reservations,19wereno–shows.Atα=0.01,testtheairlineʹsclaim.
8) Arecentstudyclaimedthatatleast15%ofjuniorhighstudentsareoverweight.Inasampleof160students,18
werefoundtobeoverweight.Atα=0.05,testtheclaim.
9) Arecentstudyclaimedthatatleast15%ofjuniorhighstudentsareoverweight.Inasampleof160students,18
werefoundtobeoverweight.Ifα=0.05,testtheclaimusingP–values.
10) Arecentstudyclaimedthatatleast15%ofjuniorhighstudentsareoverweight.Inasampleof160students,18
werefoundtobeoverweight.Ifα=0.05,testtheclaimusingconfidenceintervals.
11) Theengineeringschoolatamajoruniversityclaimsthat20%ofitsgraduatesarewomen.Inagraduatingclass
of210students,58werewomen.Doesthissuggestthattheschoolisbelievable?Useα
=0.05.
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12) Acoinistossed1000timesand570headsappear.Atα=0.05,testtheclaimthatthisisnotabiasedcoin.Does
thissuggestthecoinisfair?
13) Atelephonecompanyclaimsthat20%ofitscustomershaveatleasttwotelephonelines.Thecompanyselectsa
randomsampleof500customersandfindsthat88havetwoormoretelephonelines.Atα
=0.05,doesthedata
supporttheclaim?UseaP–value.
14) Atelephonecompanyclaimsthat20%ofitscustomershaveatleasttwotelephonelines.Thecompanyselects
arandomsampleof500customersandfindsthat88havetwoormoretelephonelines.Ifα
=0.05,testthe
companyʹsclaimusingcriticalvaluesandrejectionregions.
15) Atelephonecompanyclaimsthat20%ofitscustomershaveatleasttwotelephonelines.Thecompanyselects
arandomsampleof500customersandfindsthat88havetwoormoretelephonelines.Ifα
=0.05,testthe
companyʹsclaimusingconfidenceintervals.
16) Acoinistossed1000timesand530headsappear.Atα=0.05,testtheclaimthatthisisnotabiasedcoin.Usea
P–value.Doesthissuggestthecoinisfair?
7.5 HypothesisTestingforVarianceandStandardDeviatio
n
1 FindCriticalValues
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) FindthecriticalX2–valuestotesttheclaimσ2=4.3ifn=12andα=0.05.
A) 3.816,21.920 B) 2.603,26.757 C) 3.053,24.725 D) 4.575,19.675
2) FindthecriticalX2–valuetotesttheclaimσ2≥1.8ifn=15andα=0.05.
A) 6.571 B) 4.075 C) 4.660 D) 5.629
3) FindthecriticalX2–valuetotesttheclaimσ2≤3.2ifn=20andα=0.01.
A) 36.191 B) 27.204 C) 30.144 D) 32.852
4) FindthecriticalX2–valuetotesttheclaimσ2>1.9ifn=18andα=0.01.
A) 33.409 B) 27.587 C) 30.181 D) 35.718
5) FindthecriticalX2–valuetotesttheclaimσ2<5.6ifn=28andα=0.10.
A) 18.114 B) 14.573 C) 16.151 D) 36.741
6) FindthecriticalX2–valuestotesttheclaimσ2≠6.8ifn=10andα=0.01.
A) 1.735,23.589 B) 2.088,21.666 C) 2.700,19.023 D) 3.325,16.919
2 TestClaimsAboutVariancesandStandardDeviations
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
7) Computethestandardizedteststatistic,X2,totesttheclaimσ2=21.5ifn=12,s2=18,andα=0.05.
A) 9.209 B) 12.961 C) 18.490 D) 0.492
8) Computethestandardizedteststatistic,X2,totesttheclaimσ2≥14.4ifn=15,s2=12,andα=0.05.
A) 11.667 B) 8.713 C) 12.823 D) 23.891
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9) Computethestandardizedteststatistic,X2,totesttheclaimσ2≤28.8ifn=20,s2=55.8,andα=0.01.
A) 36.813 B) 9.322 C) 12.82 D) 33.41
10) Computethestandardizedteststatistic,X2,totesttheclaimσ2>1.9ifn=18,s2=2.7,andα=0.01.
A) 24.158 B) 28.175 C) 33.233 D) 43.156
11) Computethestandardizedteststatistic,X2,totesttheclaimσ2<50.4ifn=28,s2=31.5,andα=0.10.
A) 16.875 B) 14.324 C) 18.132 D) 21.478
12) Computethestandardizedteststatistic,X2totesttheclaimσ2≠61.2ifn=10,s2=67.5,andα=0.01.
A) 9.926 B) 3.276 C) 4.919 D) 12.008
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
13) Testtheclaimthatσ2=4.3ifn=12,s2=3.6andα=0.05.Assumethatthepopulationisnormallydistributed.
14) Testtheclaimthatσ2≥1.8ifn=15,s2=1.5,andα=0.05.Assumethatthepopulationisnormallydistributed.
15) Testtheclaimthatσ2≤3.2ifn=20,s2=6.2,andα=0.01.Assumethatthepopulationisnormallydistributed.
16) Testtheclaimthatσ2>17.1ifn=18,s2=24.3,andα=0.01.Assumethatthepopulationisnormally
distributed.
17) Testtheclaimthatσ2<39.2ifn=28,s2=24.5,andα=0.10.Assumethatthepopulationisnormally
distributed.
18) Testtheclaimthatσ2≠6.8ifn=10,s2=7.5,andα=0.01.Assumethatthepopulationisnormallydistributed.
19) Testtheclaimthatσ=10.35ifn=12,s=9.5
andα =0.05.Assumethatthepopulationisnormallydistributed.
20) Testtheclaimthatσ≥12.06ifn=15,s=10.98
andα =0.05.Assumethatthepopulationisnormally
distributed.
21) Testtheclaimthatσ≤1.79ifn=20,s=2.49
andα =0.01.Assumethatthepopulationisnormallydistributed.
22) Testtheclaimthatσ>5.52ifn=18,s=6.56
andα =0.01.Assumethatthepopulationisnormallydistributed.
23) Testtheclaimthatσ<4.74ifn=28,s=3.74 andα =0.10.Assumethatthepopulationisnormallydistributed.
24) Testtheclaimthatσ≠10.44ifn=10,s=10.96
andα =0.01.Assumethatthepopulationisnormally
distributed.
25) Listedbelowisthenumberofticketsissuedbyalocalpolicedepartment.Assumingthatthedataisnormally
distributed,testtheclaimthatthestandarddeviationforthedatais15tickets.Useα
=0.01.
70 48 41 68 69 55 70
57 60 83 32 60 72 58
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26) Theheights(ininches)of20randomlyselectedadultmalesarelistedbelow.Testtheclaimthatthevarianceis
lessthan6.25.Useα=0.05.Assumethepopulationisnormallydistributed.
70727170697369687071
67717074696871717172
27) Theheights(ininches)of20randomlyselectedadultmalesarelistedbelow.Testtheclaimthatthevarianceis
lessthan6.25.Assumethepopulationisnormallydistributed.Useα=0.05andconfidenceintervals.
70 72 71 70 69 73 69 68 70 71
67 71 70 74 69 68 71 71 71 72
28) Atruckingfirmsuspectsthatthevarianceforacertaintireisgreaterthan1,000,000.Tochecktheclaim,the
firmputs101ofthesetiresonitstrucksandgetsastandarddeviationof1200miles.Atα
=0.05,testthe
truckingfirmʹsclaim.
29) Atruckingfirmsuspectsthatthevarianceforacertaintireisgreaterthan1,000,000.Tochecktheclaim,the
firmputs101ofthesetiresonitstrucksandgetsastandarddeviationof1200miles.Ifα
=0.05,testthe
truckingfirmʹsclaimusingconfidenceintervals.
30) Alocalbankneedsinformationconcerningthestandarddeviationofthecheckingaccountbalancesofits
customers.Frompreviousinformationitwasassumedtobe$250.Arandomsampleof61accountswas
checked.Thestandarddeviationwas$286.20.Atα=0.01,testthebankʹsassumption.Assumethattheaccount
balancesarenormallydistributed.
31) Inonearea,monthlyincomesofcollegegraduateshaveastandarddeviationof$650.Itisbelievedthatthe
standarddeviationofmonthlyincomesofnon–collegegraduatesishigher.Asampleof71non–college
graduatesarerandomlyselectedandfoundtohaveastandarddeviationof$950.Testtheclaimthat
non–collegegraduateshaveahigherstandarddeviation.Useα=0.05.
32) Astatisticsprofessoratanall–womenʹscollegedeterminedthatthestandarddeviationofwomenʹsheightsis
2.5inches.Theprofessorthenrandomlyselected41malestudentsfromanearbyall–malecollegeandfound
thestandarddeviationtobe2.9inches.Testtheprofessorʹsclaimthatthestandarddeviationofmaleheightsis
greaterthan2.5inches.Useα=0.01.
3 TestClaimsAboutVariancesandStandardDeviationsUsingaP–value
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
33) Theheights(ininches)of20randomlyselectedadultmalesarelistedbelow.Testtheclaimthatthevarianceis
lessthan6.25.Assumethepopulationisnormallydistributed.Useα=0.05andP–values.
70 72 71 70 69 73 69 68 70 71
67 71 70 74 69 68 71 71 71 72
34) Atruckingfirmsuspectsthatthevarianceforacertaintireisgreaterthan1,000,000.Tochecktheclaim,the
firmputs101ofthesetiresonitstrucksandgetsastandarddeviationof1200miles.Ifα
=0.05,testthe
truckingfirmʹsclaimusingP–values.
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Ch.7 HypothesisTestingwithOneSample
AnswerKey
7.1 IntroductiontoHypothesisTestin
g
1 StateaNullandAlternativeHypothesis
2 IdentifyWhethertoUseaOne–tailedorTwo–tailedTest
3 IdentifyTypeIandTypeIIErrors
5 UseConfidenceIntervalstoMakeDecisions
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6 Concepts
7.2 HypothesisTestingfortheMean(LargeSamples)
1 FindP–values
2 TestaClaimAboutaMeanUsingP–values
3 FindCriticalValues
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7.3 HypothesisTestingfortheMean(SmallSamples)
1 FindCriticalValuesinat–distribution
2 TestaClaimAboutaMean
3 TestaClaimAboutaMeanUsingaP–value
7.4 HypothesisTestingforProportions
1 TestaClaimAboutaProportion
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7.5 HypothesisTestingforVarianceandStandardDeviatio
n
1 FindCriticalValues
2 TestClaimsAboutVariancesandStandardDeviations
Page149
3 TestClaimsAboutVariancesandStandardDeviationsUsingaP–value
Page150