Economics Chapter 10 Recently Customer Made Claim That The Proshop

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Ch.10 HypothesisTestsRegardingaParameter

10.1 TheLanguageofHypothesisTesting

1 Determinethenullandalternativehypotheses.

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

Thenullandalternativehypothesesaregiven.Determinewhetherthehypothesistestisleft –tailed,right–tailed,or

two–tailedandtheparameterthatisbeingtested.

1) H 0:μ=8.6

H1:μ≠8.6

A) Two–tailed,μ B) Two–tailed,xC) Right–tailed,μ D) Left–tailed,x

2) H 0:p=0.82

H1:p>0.82

A) Right–tailed,p B) Left–tailed,p C) Right–tailed,p

D) Left–tailed,p

3) H 0:σ=8.6

H1:σ<8.6

A) Left–tailed,σ B) Right–tailed,μ C) Right–tailed,σ D) Left–tailed,s

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

Provideanappropriateresponse.

4) ThemeanannualreturnforanemployeeʹsIRAisatmost3.4 percent.Writethenullandalternative

hypotheses.

5) ThemeanageoflawyersinNewYorkis50.7 years.Writethenullandalternativehypotheses.

6) Themeanrepairbillofcarsisgreaterthan$110.Writethenullandalternativehypotheses.

7) Themeanutilitybillinonecityduringthesummerwaslessthan$90.Writethenullandalternative

hypotheses.

8) ThemeanannualreturnforanemployeeʹsIRAisatmost4.7 percent.Writethenullandalternative

hypotheses.

9) Apopularreferendumontheballotisfavoredbymorethanhalfofthevoters.Writethenullandalternative

hypotheses.

10) TheownerofanoutdoorstorerecommendsagainstbuyingthenewmodelofonebrandofGPSreceivers

becausetheyvarymorethantheoldmodel,whichhadastandarddeviationof50meters.Writethenulland

alternativehypotheses.

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

11) A______________isastatementorclaimregardingacharacteristicofoneormorepopulations.

A) hypothesis B) conclusion C) conjecture D) fact

12) The______________hypothesiscontainstheʺ=ʺsign.

A) null B) alternative C) explanatory D) conditional

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13) Ahypothesistestisaʺtwo–tailedʺifthealternativehypothesiscontainsa_______sign.

A) ≠B) +C) <D) >

2 ExplainTypeIandTypeIIerrors.

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

Provideanappropriateresponse.

1) ThemeanageofjudgesinLosAngelesis48.6 years.IdentifythetypeIandtypeIIerrorsforthehypothesistest

ofthisclaim.

2) Themeancostoftextbooksforoneclassisgreaterthan$140.IdentifythetypeIandtypeIIerrorsforthe

hypothesistestofthisclaim.

3) Themeanmonthlycellphonebillforonehouseholdwaslessthan$93.IdentifythetypeIandtypeIIerrorsfor

thehypothesistestofthisclaim.

4) Areferendumforanupcomingelectionisfavoredbymorethanhalfofthevoters.IdentifythetypeIandtype

IIerrorsforthehypothesistestofthisclaim.

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

5) Alocaltennispro–shopstringstennisracketsatthetension(poundspersquareinch)requestedbythe

customer.Recentlyacustomermadeaclaimthatthepro–shopconsistentlystringsracketsatlowertensions,on

average,thanrequested.Tosupportthisclaim,thecustomeraskedtheproshoptostring12newracketsat53

psi.Uponreceivingtherackets,thecustomermeasuredthetensionofeachandcalculatedthefollowing

summarystatistics:x=51psi,s=2.4psi.Inordertoconductthetest,thecustomerselectedasignificancelevel

ofα=.05.Interpretthisvalue.

A) Theprobabilityofconcludingthatthetruemeanislessthan53 psiwheninfactitisequalto53 psiisonly

.05.

B) ThesmallestvalueofαthatyoucanuseandstillrejectH0is0.05.

C) TheprobabilityofmakingaTypeIIerroris0.95.

D) Thereisa5%chancethatthesamplewillbebiased.

6) TrueorFalse:IfIspecifyβtobeequalto0.36

thenthevalueofα mustbe0.64.

A) False B) True

7) WhatistheprobabilityassociatedwithnotmakingaTypeIIerror?

A) (1–β)B)αC) βD) (1–α)

8) WeneverconcludeʺAcceptH0ʺinatestofhypothesis.Thisisbecause:

A) β=p(TypeIIerror)isnotknown. B) αistheprobabilityofaTypeIerror.

C) Therejectionregionisnotknown. D) Thep–valueisnotsmallenough.

9) Ifwerejectthenullhypothesiswhenthenullhypothesisistrue,thenwehavemadea

A) TypeIerror B) TypeIIerror C) Correctdecision D) Typeα error

10) Ifwedonotrejectthenullhypothesiswhenthenullhypothesisisinerror,thenwehavemadea

A) TypeIIerror B) TypeIerror C) Correctdecision D) Typeβ error

11) Thelevelofsignificance,α

istheprobabilityofmakinga

A) TypeIerror B) TypeIIerror C) Correctdecision D) Typeβ error

12) TrueorFalse:TypeIandTypeIIerrorsareindependentevents.

A) False B) True

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3 Stateconclusionstohypothesistests.

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

Provideanappropriateresponse.

1) Themeanageofprincipalsinalocalschooldistrictis50.2 years.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μ =50.2.

B) Thereisnotsufficientevidencetorejecttheclaimμ =50.2.

C) Thereissufficientevidencetosupporttheclaimμ=50.2.

D) Thereisnotsufficientevidencetosupporttheclaimμ =50.2.

2) Themeanageofprofessorsatauniversityis57.9 years.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rejecttheclaimμ =57.9.

B) Thereissufficientevidencetorejecttheclaimμ =57.9.

C) Thereissufficientevidencetosupporttheclaimμ=57.9.

D) Thereisnotsufficientevidencetosupporttheclaimμ =57.9.

3) Themeanageofprofessorsatauniversityisgreaterthan58.3 years.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μ>58.3.

B) Thereissufficientevidencetorejecttheclaimμ >58.3.

C) Thereisnotsufficientevidencetorejecttheclaimμ >58.3.

D) Thereisnotsufficientevidencetosupporttheclaimμ >58.3.

4) ThemeanageofjudgesinDallasisgreaterthan50.2 years.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μ >50.2.

B) Thereissufficientevidencetorejecttheclaimμ >50.2.

C) Thereisnotsufficientevidencetorejecttheclaimμ >50.2.

D) Thereissufficientevidencetosupporttheclaimμ>50.2.

5) Themeanmonthlygasolinebillforonehouseholdisgreaterthan$150.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μ>$150.

B) Thereissufficientevidencetorejecttheclaimμ >$150.

C) Thereisnotsufficientevidencetorejecttheclaimμ >$150.

D) Thereisnotsufficientevidencetosupporttheclaimμ >$150.

6) Themeanmonthlygasolinebillforonehouseholdisgreaterthan$160.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μ >$160.

B) Thereissufficientevidencetorejecttheclaimμ >$160.

C) Thereisnotsufficientevidencetorejecttheclaimμ >$160.

D) Thereissufficientevidencetosupporttheclaimμ>$160.

7) ThemeannumberofrushingyardsforoneNFLteamwaslessthan99 yardspergame.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μ<99.

B) Thereissufficientevidencetorejecttheclaimμ <99.

C) Thereisnotsufficientevidencetorejecttheclaimμ <99.

D) Thereisnotsufficientevidencetosupporttheclaimμ <99.

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8) ThemeannumberofrushingyardsforoneNFLteamwaslessthan109 yardspergame.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μ <109.

B) Thereissufficientevidencetorejecttheclaimμ <109.

C) Thereisnotsufficientevidencetorejecttheclaimμ <109.

D) Thereissufficientevidencetosupporttheclaimμ<109.

9) ThedeanofamajoruniversityclaimsthatthemeannumberofhoursstudentsstudyatherUniversity(per

day)isatmost3.6hours.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μ ≤3.6.

B) Thereisnotsufficientevidencetorejecttheclaimμ ≤3.6.

C) Thereissufficientevidencetosupporttheclaimμ≤3.6.

D) Thereisnotsufficientevidencetosupporttheclaimμ ≤3.6.

10) ThedeanofamajoruniversityclaimsthatthemeannumberofhoursstudentsstudyatherUniversity(per

day)isatmost4.4hours.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rejecttheclaimμ ≤4.4.

B) Thereissufficientevidencetorejecttheclaimμ ≤4.4.

C) Thereissufficientevidencetosupporttheclaimμ≤4.4.

D) Thereisnotsufficientevidencetosupporttheclaimμ ≤4.4.

11) Acandidateforstaterepresentativeofacertainstateclaimstobefavoredbyatleasthalfofthevoters.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p≥0.5.

B) Thereisnotsufficientevidencetorejecttheclaimp≥0.5.

C) Thereissufficientevidencetosupporttheclaimp≥0.5.

D) Thereisnotsufficientevidencetosupporttheclaimp≥0.5.

12) Acandidateforstaterepresentativeofacertainstateclaimstobefavoredbyatleasthalfofthevoters.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rejecttheclaimp≥0.5.

B) Thereissufficientevidencetorejecttheclaimp≥0.5.

C) Thereissufficientevidencetosupporttheclaimp≥0.5.

D) Thereisnotsufficientevidencetosupporttheclaimp≥0.5.

10.2 HypothesisTestsforaPopulationProportio

1 Explainthelogicofhypothesistesting.

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

Provideanappropriateresponse.

1) Findthecriticalvalueforaleft–tailedtestwithα =0.025.

A) –1.96 B) –2.24 C) –1.645 D) –2.575

2) Findthecriticalvalueforatwo–tailedtestwithα =0.08.

A) ±1.75 B) ±1.405 C) ±2.65 D) ±1.96

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3) Supposeyouwanttotesttheclaimthatμ=3.5.Givenasamplesizeofn=48 andalevelofsignificanceof

α=0.01,whenshouldyourejectH0?

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

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

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

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

4) Supposeyouwanttotesttheclaimthatμ>25.6.Givenasamplesizeofn=53 andalevelofsignificanceof

α=0.01,whenshouldyourejectH0?

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2.575.

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

5) Supposeyouwanttotesttheclaimthatμ≥65.4.Givenasamplesizeofn=35andalevelofsignificanceof

α=0.01,whenshouldyourejectH0?

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

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

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

D) RejectH0ifthestandardizedteststatisticislessthan–1.28.

6) Whentheresultsofahypothesistestaredeterminedtobestatisticallysignificant,thenwe_______________the

nullhypothesis.

A) reject B) failtoreject C) polarize D) compartmentalize

2 Testhypothesesaboutapopulationproportion.

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

Provideanappropriateresponse.

1) Thebusinesscollegecomputingcenterwantstodeterminetheproportionofbusinessstudentswhohave

personalcomputers(PCʹs)athome.Iftheproportionexceeds35%,thenthelabwillscalebackaproposed

enlargementofitsfacilities.Suppose300businessstudentswererandomlysampledand85havePCʹsathome.

Findtherejectionregionforthistestusingα=0.10.

A) RejectH0ifz>1.28. B) RejectH0ifz< –1.28.

C) RejectH0ifz>1.645orz<–1.645. D) RejectH0ifz=1.28.

2) Thebusinesscollegecomputingcenterwantstodeterminetheproportionofbusinessstudentswhohave

personalcomputers(PCʹs)athome.Iftheproportiondiffersfrom35%,thenthelabwillmodifyaproposed

enlargementofitsfacilities.Supposeahypothesistestisconductedandtheteststatisticis2.6.FindtheP–value

foratwo–tailedtestofhypothesis.

A) 0.0094 B) 0.0047 C) 0.4906 D) 0.4953

3) Thebusinesscollegecomputingcenterwantstodeterminetheproportionofbusinessstudentswhohave

personalcomputers(PCʹs)athome.Iftheproportionexceeds30%,thenthelabwillscalebackaproposed

enlargementofitsfacilities.Suppose300businessstudentswererandomlysampledand65havePCʹsathome.

Whatassumptionsarenecessaryforthistesttobesatisfied?

A) Noassumptionsarenecessary.

B) Thesamplevarianceequalsthepopulationvariance.

C) Thepopulationhasanapproximatelynormaldistribution.

D) Thesamplemeanequalsthepopulationmean.

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4) Asurveyclaimsthat9outof10doctors(i.e.,90%)recommendbrandZfortheirpatientswhohavechildren.To

testthisclaimagainstthealternativethattheactualproportionofdoctorswhorecommendbrandZislessthan

90%,arandomsampleof100doctorsresultsin83whoindicatethattheyrecommendbrandZ.Theteststatistic

inthisproblemisapproximately(roundtothenearesthundredth):

A) –2.33 B) 2.33 C) –1.83 D) –1.99

5) Asurveyclaimsthat9outof10doctors(i.e.,90%)recommendbrandZfortheirpatientswhohavechildren.To

testthisclaimagainstthealternativethattheactualproportionofdoctorswhorecommendbrandZislessthan

90%,arandomsampleofdoctorswastaken.Supposetheteststatisticisz=–2.23.CanweconcludethatH0

shouldberejectedatthea)α=0.10,b)α=0.05,andc)α=0.01level?

A) a)yes;b)yes;c)no B) a)yes;b)yes;c)yes

C) a)no;b)no;c)no D) a)no;b)no;c)yes

6) Anationwidesurveyclaimedthatatleast55%ofparentswithyoungchildrencondonespankingtheirchildas

aregularformofpunishment.Inarandomsampleof100parentswithyoungchildren,howmanywouldneed

tosaythattheycondonespankingasaformofpunishmentinordertorefutetheclaimatα

=0.5?

A) Youwouldneed46orlessparentstosupportspankingtorefutetheclaim.

B) Youwouldneedexactly46parentstosupportspankingtorefutetheclaim.

C) Youwouldneed47orlessparentstosupportspankingtorefutetheclaim.

D) Youwouldneedmorethan46parentstosupportspankingtorefutetheclaim.

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

7) Amethodcurrentlyusedbydoctorstoscreenwomenforpossiblebreastcancerfailstodetectcancerin15%of

thewomenwhoactuallyhavethedisease.Anewmethodhasbeendevelopedthatresearchershopewillbe

abletodetectcancermoreaccurately.Arandomsampleof70womenknowntohavebreastcancerwere

screenedusingthenewmethod.Ofthese,thenewmethodfailedtodetectcancerin8.Calculatethetest

statisticusedbytheresearchersforthistestofhypothesis.Roundtothenearestthousandth.

8) Amethodcurrentlyusedbydoctorstoscreenwomenforpossiblebreastcancerfailstodetectcancerin15%of

thewomenwhoactuallyhavethedisease.Anewmethodhasbeendevelopedthatresearchershopewillbe

abletodetectcancermoreaccurately.Arandomsampleof80womenknowntohavebreastcancerwere

screenedusingthenewmethod.Ofthese,thenewmethodfailedtodetectcancerin9.Isthesamplesize

sufficientlylargeinordertoconductthistestofhypothesis?Explain.Roundtothenearestthousandth.

9) Increasingnumbersofbusinessesareofferingchild–carebenefitsfortheirworkers.However,oneunionclaims

thatmorethan85%offirmsinthemanufacturingsectorstilldonotofferanychild–carebenefitstotheir

workers.Arandomsampleof430manufacturingfirmsisselected,andonly32ofthemofferchild–care

benefits.Specifytherejectionregionthattheunionwillusewhentestingatα

=0.10.

10) Increasingnumbersofbusinessesareofferingchild–carebenefitsfortheirworkers.However,oneunionclaims

thatmorethan80%offirmsinthemanufacturingsectorstilldonotofferanychild–carebenefitstotheir

workers.Arandomsampleof390manufacturingfirmsisselectedandaskediftheyofferchild –carebenefits.

SupposetheP–valueforthistestwasreportedtobep=0.1112.Statetheconclusionofinteresttotheunion.

Useα=0.10.

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

11) Inasample,76peopleor38%ofthepeopleinthesamplesaidthatthemayorshouldbeprosecutedfor

misconduct.Howmanypeoplewhereinthesample?

A) 200 B) 29 C) 105 D) 50

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12) Determinethecriticalvalue,z0

totesttheclaimaboutthepopulationproportionp=0.250givenn=48 and

^=0.231.Useα=0.01.

A) ±2.575 B) ±1.96 C) ±1.645 D) ±2.33

13) Determinethestandardizedteststatistic,z,totesttheclaimaboutthepopulationproportionp≥0.132 given

n=48andp

^=0.11.Useα=0.05.

A) –0.45 B) –1.645 C) –0.568 D) –0.124

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

14) Testtheclaimaboutthepopulationproportionp≥0.700givenn=50andp

=0.612.Useα=0.10.

15) FiftypercentofregisteredvotersinacongressionaldistrictareregisteredDemocrats.TheRepublicancandidate

takesapolltoassesshischancesinatwo–candidaterace.Hepolls1200potentialvotersandfindsthat621plan

tovotefortheDemocraticcandidate.DoestheRepublicancandidatehaveachancetowin?Useα

=0.05.

16) Anairlineclaimsthattheno–showrateforpassengersislessthan5%.Inasampleof420randomlyselected

reservations,19wereno–shows.Atα=0.01,testtheairlineʹsclaim.Roundp

^tothenearestthousandthwhen

calculatingtheteststatistic.

17) Arecentstudyclaimedthatatleast15%ofjuniorhighstudentsareoverweight.Inasampleof160students,18

werefoundtobeoverweight.Atα=0.05,testtheclaim.

18) Theengineeringschoolatamajoruniversityclaimsthat20%ofitsgraduatesarewomen.Inagraduatingclass

of210students,58werefemales.Doesthissuggestthattheschoolisbelievable?Useα

=0.05.Roundp

^tothe

nearestten–thousandthwhencalculatingtheteststatistic.

19) Acoinistossed1000timesand570headsappear.Atα=0.05,testtheclaimthatthisisnotabiasedcoin.

20) Inonecity,25outof100randomlysampledteenagerssaythattheysmoke.

(a)ConsiderthehypothesesH0:p=0.22versusH1:p>0.22.Explainwhattheresearcherwouldbetesting.

Performthetestattheα=0.05levelofsignificance.Writeaconclusionforthetest.Roundtheteststatisticto

thenearesthundredth.

(b)Repeatpart(a)forthehypothesesH0:p=0.24versusH1:p>0.24.

(c)Basedonyourresultsinparts(a)and(b),writeafewsentencesthatexplainthedifferencebetween

ʺacceptingʺthestatementinthenullhypothesisversusʺnotrejectingʺthestatementinthenullhypothesis.

3 Testhypothesesaboutapopulationproportionusingthebinomialprobabilitydistribution.

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

Provideanappropriateresponse.

1) Accordingtoanationalstatisticsbureau,3.7%ofmaleslivingintheSouthwestwereretiredexterminators.A

researcherbelievesthatthepercentagehasincreasedsincethen.Sherandomlyselects250malesinthe

Southwestandfindsthat4ofthemareretiredexterminators.Testthisresearcherʹsclaimattheα

=0.1levelof

significance.

2) Accordingtoaprestigioushistoricalsociety,in1999,7.2%ofrecenthighschoolgraduatesbelievethatthe

Romansinventedmayonnaise.Aclassicsscholarbelievesthatthepercentagehasincreasedsincethen.He

randomlyselects125recenthighschoolgraduatesandfindsthat17ofthembelieveintheRomaninventionof

mayonnaise.Testthisresearcherʹsclaimattheα=0.01levelofsignificance.

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3) Accordingtoalocalchamberofcommerce,in1993,5.9%oflocalarearesidentsownedmorethanfivecars.A

localcardealerclaimsthatthepercentagehasincreased.Herandomlyselects180localarearesidentsandfinds

that12ofthemownmorethanfivecars.Testthiscardealerʹsclaimattheα

=0.05levelofsignificance.

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

4) Aneventisconsideredunusualiftheprobabilityofobservingtheeventis

A) lessthan0.05 B) lessthan0.025 C) lessthan0.10 D) greaterthan0.95

10.3 HypothesisTestsforaPopulationMean

1 Testhypothesesaboutamean.

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

Findthecriticalvalue.

1) Determinethecriticalvalueforaright–tailedtestofapopulationmeanattheα=0.001levelofsignificance

with15degreesoffreedom.

A) 3.733 B) 2.602 C) –3.733 D) 3.787

2) Determinethecriticalvalueforaleft–tailedtestofapopulationmeanattheα=0.005levelofsignificance

basedonasamplesizeofn=30.

A) –2.756 B) –1.699 C) 2.756 D) 2.750

3) Determinethecriticalvaluesforatwo–tailedtestofapopulationmeanattheα=0.01levelofsignificance

basedonasamplesizeofn=29.

A) ±2.763 B) ±2.756 C) ±2.467 D) ±2.462

Provideanappropriateresponse.

4) Arelativefrequencyhistogramforthesalepricesofhomessoldinonecityduring2010isshownbelow.Based

onthehistogram,isalargesamplenecessarytoconductahypothesistestaboutthemeansaleprice?Ifso,

why?

A) Yes;datadonotappeartobenormallydistributedbutskewedright.

B) Yes;datadonotappeartobenormallydistributedbutskewedleft.

C) No;dataappeartobenormallydistributed.

D) Yes;datadonotappeartobenormallydistributedbutbimodal.

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5) Theagesofagroupofpatientsbeingtreatedatonehospitalforosteoporosisaresummarizedinthefrequency

histogrambelow.Basedonthehistogram,isalargesamplenecessarytoconductahypothesistestaboutthe

meanage?Ifso,why?

A) Yes;datadonotappeartobenormallydistributedbutskewedleft.

B) Yes;datadonotappeartobenormallydistributedbutskewedright.

C) Yes;datadonotappeartobenormallydistributedbutbimodal.

D) No;dataappeartobenormallydistributedwithnooutliers.

6) Theweeklysalaries(indollars)ofrandomlyselectedemployeesofacompanyaresummarizedintheboxplot

below.Basedontheboxplot,isalargesamplenecessarytoconductahypothesistestaboutthemeansalary?If

so,why?

A) Yes;datadonotappeartobenormallydistributedbutskewedright.

B) Yes;datadonotappeartobenormallydistributedbutskewedleft.

C) No;dataappeartobenormallydistributed.

D) Yes;datacontainoutliers.

7) Theweights(inounces)ofasampleoftomatoesofaparticularvarietyaresummarizedintheboxplotbelow.

Basedontheboxplot,isalargesamplenecessarytoconductahypothesistestaboutthemeanweight?Ifso,

why?

A) Yes;datacontainoutliers.

B) Yes;datadonotappeartobenormallydistributedbutskewedleft.

C) Yes;datadonotappeartobenormallydistributedbutskewedright.

D) No;dataappeartobenormallydistributedwithnooutliers.

8) Findthestandardizedteststatistictforasamplewithn=12,x=30.2,s=2.2,andα=0.01ifH0:μ=29.Round

youranswertothreedecimalplaces.

A) 1.890 B) 1.991 C) 2.132 D) 2.001

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9) Findthestandardizedteststatistictforasamplewithn=10,x=7.9,s=1.3,andα=0.05ifH0:μ≥8.8.Round

youranswertothreedecimalplaces.

A) –2.189 B) –3.186 C) –3.010 D) –2.617

10) Findthestandardizedteststatistictforasamplewithn=15,x=10.1,s=0.8,andα=0.05ifH0:μ≤9.8.Round

youranswertothreedecimalplaces.

A) 1.452 B) 1.728 C) 1.631 D) 1.312

11) Findthestandardizedteststatistictforasamplewithn=20,x=13.3,s=2.0,andα=0.05ifH1:μ<13.7.

Roundyouranswertothreedecimalplaces.

A) –0.894 B) –0.872 C) –1.265 D) –1.233

12) Findthestandardizedteststatistictforasamplewithn=25,x=14,s=3,andα=0.005ifH1:μ>13.Round

youranswertothreedecimalplaces.

A) 1.667 B) 1.997 C) 1.452 D) 1.239

13) Findthestandardizedteststatistictforasamplewithn=12,x=15.7,s=2.1,andα=0.01ifH1:μ≠16.2.

Roundyouranswertothreedecimalplaces.

A) –0.825 B) –0.008 C) –0.037 D) –0.381

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

14) Useat–testtotesttheclaimμ=10atα=0.01,giventhesamplestatisticsn=12,x=11.2,ands=2.2.Round

theteststatistictothenearestthousandth.

15) Useat–testtotesttheclaimμ≥9.7atα=0.05,giventhesamplestatisticsn=10,x=8.8,ands=1.3.Roundthe

teststatistictothenearestthousandth.

16) Useat–testtotesttheclaimμ≤8.9atα=0.05,giventhesamplestatisticsn=15,x=9.2,ands=0.8.Roundthe

teststatistictothenearestthousandth.

17) Useat–testtotesttheclaimμ<12.6atα=0.10,giventhesamplestatisticsn=20,x=12.2,ands=2.0.Round

theteststatistictothenearestthousandth.

18) Useat–testtotesttheclaimμ>34atα=0.005,giventhesamplestatisticsn=25,x=35,ands=3.Roundthe

teststatistictothenearestthousandth.

19) Useat–testtotesttheclaimμ=19.4atα=0.01,giventhesamplestatisticsn=12,x=18.9,ands=2.1.Round

theteststatistictothenearestthousandth.

20) Alocalretailerclaimsthatthemeanwaitingtimeislessthan9 minutes.Arandomsampleof20waitingtimes

hasameanof7.4minuteswithastandarddeviationof2.1minutes.Atα=0.01,testtheretailerʹsclaim.

Assumethedistributionisnormallydistributed.Roundtheteststatistictothenearestthousandth.

21) Amanufacturerclaimsthatthemeanlifetimeofitslithiumbatteriesis1400 hours.Ahomeownerselects25of

thesebatteriesandfindsthemeanlifetimetobe1380hourswithastandarddeviationof80hours.Testthe

manufacturerʹsclaim.Useα=0.05.Roundtheteststatistictothenearestthousandth.

22) Ashippingfirmsuspectsthatthemeanlifeofacertainbrandoftireusedbyitstrucksislessthan40,000 miles.

Tochecktheclaim,thefirmrandomlyselectsandtests18ofthesetiresandgetsameanlifetimeof39,300miles

withastandarddeviationof1200miles.Atα

=0.05,testtheshippingfirmʹsclaim.Roundtheteststatisticto

thenearestthousandth.

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23) Alocaljuicemanufacturerdistributesjuiceinbottleslabeled12ounces.Agovernmentagencythinksthatthe

companyischeatingitscustomers.Theagencyselects20ofthesebottles,measurestheircontents,andobtainsa

samplemeanof11.7ounceswithastandarddeviationof0.7ounce.Usea0.01significanceleveltotestthe

agencyʹsclaimthatthecompanyischeatingitscustomers.Roundtheteststatistictothenearestthousandth.

24) Alocalgroupclaimsthatthepoliceissueatleast60parkingticketsadayintheirarea.Toprovetheirpoint,

theyrandomlyselecttwoweeks.Theirresearchyieldsthenumberofticketsissuedforeachday.Thedataare

listedbelow.Atα=0.01,testthegroupʹsclaim.Roundtheteststatistictothenearestthousandth.

70 48 41 68 69 55 70 57 60 83

32 60 72 58

25) Abankclaimsthatthemeanwaitingtimeinlineislessthan4.3 minutes.Arandomsampleof20customershas

ameanof4.1minuteswithastandarddeviationof0.8minute.Ifα=0.05,testthebankʹsclaimusingP–values.

26) Alocalhardwarestoreclaimsthatthemeanwaitingtimeinlineislessthan3.5minutes.Arandomsampleof

20customershasameanof3.7minuteswithastandarddeviationof0.8minute.Ifα

=0.05,testthestoreʹs

claimusingP–values.

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

27) Alocaleat–inpizzarestaurantwantstoinvestigatethepossibilityofstartingtodeliverpizzas.Theownerof

thestorehasdeterminedthathomedeliverywillbesuccessfuliftheaveragetimespentonthedeliveriesdoes

notexceed32minutes.Theownerhasrandomlyselected23customersandhasdeliveredpizzastotheirhomes

inordertotestifthemeandeliverytimeactuallyexceeds32minutes.SupposetheP–valueforthetestwas

foundtobe0.0297.Statethecorrectconclusion.

A) Atα=0.025,wefailtorejectH0.B)Atα =0.05,wefailtorejectH0.

C) Atα=0.02,werejectH0.D)Atα =0.03,wefailtorejectH0.

28) Alocaltennispro–shopstringstennisracketsatthetension(poundspersquareinch)requestedbythe

customer.Recentlyacustomermadeaclaimthatthepro–shopconsistentlystringsracketsatlowertensions,on

average,thanrequested.Tosupportthisclaim,thecustomeraskedtheproshoptostring13newracketsat65

psi.Supposethetwo–tailedP–valueforthetestdescribedabove(obtainedfromacomputerprintout)is0.09.

Givetheproperconclusionforthetest.Useα=0.05.

A) Thereissufficientevidencetoconcludethatμ

thetruemeantensionoftherackets,islessthan65 psi.

B) AcceptH0andconcludethatμ

thetruemeantensionoftherackets,equals65psi.

C) Thereisinsufficientevidencetoconcludethatμ

thetruemeantensionoftherackets,islessthan65 psi.

D) RejectH0andconcludethatμ

thetruemeantensionoftherackets,equals65psi.

29) Ifwehaveasampleof12drawnfromanormalpopulation,thenwewoulduseasourteststatistic

A) t0with11degreesoffreedom B) z0with11degreesoffreedom

C) t0with12degreesoffreedom D) z0with12degreesoffreedom

2 Understandthedifferencebetweenstatisticalsignificanceandpracticalsignificance.

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

Provideanappropriateresponse.

1) TrueorFalse:Resultsthatarestatisticallysignificantarealwayspracticallysignificant.

A) False B) True

2) TrueorFalse:Resultsthatarepracticallysignificantwillalwaysbestatisticallysignificant.

A) False B) True

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10.4 HypothesisTestsforaPopulationStandardDeviatio

1 Testhypothesesaboutapopulationstandarddeviation.

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

Findthecriticalvalue(s).

1) Determinethecriticalvalueforaright–tailedtestofapopulationstandarddeviationwith22degreesof

freedomattheα=0.05levelofsignificance.

A) 33.924 B) 32.671 C) 42.796 D) 12.338

2) Determinethecriticalvalueforaleft–tailedtestofapopulationstandarddeviationforasampleofsizen=21

attheα=0.05levelofsignificance.

A) 10.851 B) 11.591 C) 31.41 D) 32.671

3) Determinethecriticalvaluesforatwo–tailedtestofapopulationstandarddeviationforasampleofsizen=7

attheα=0.1levelofsignificance.

A) 1.635

12.592 B) 2.167

14.067 C) 2.204

10.645 D) 2.833

12.017

Provideanappropriateresponse.Roundtheteststatistictothenearestthousandth.

4) Computethestandardizedteststatistic,χ2,totesttheclaimσ2=30.1ifn=12,s2=25.2,andα=0.05.

A) 9.209 B) 12.961 C) 18.490 D) 0.492

5) Computethestandardizedteststatistic,χ2,totesttheclaimσ2≥7.2ifn=15,s2=6,andα=0.05.

A) 11.667 B) 8.713 C) 12.823 D) 23.891

6) Computethestandardizedteststatistic,χ2,totesttheclaimσ2≤25.6ifn=20,s2=49.6,andα=0.01.

A) 36.813 B) 9.322 C) 12.82 D) 33.41

7) Computethestandardizedteststatistic,χ2,totesttheclaimσ2>15.2ifn=18,s2=21.6,andα=0.01.

A) 24.158 B) 28.175 C) 33.233 D) 43.156

8) Computethestandardizedteststatistic,χ2,totesttheclaimσ2<50.4ifn=28,s2=31.5,andα=0.10.

A) 16.875 B) 14.324 C) 18.132 D) 21.478

9) Computethestandardizedteststatistic,χ2totesttheclaimσ2≠20.4ifn=10,s2=22.5,andα=0.01.

A) 9.926 B) 3.276 C) 4.919 D) 12.008

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

10) Testtheclaimthatσ2=30.1ifn=12,s2=25.2andα=0.05.Assumethatthepopulationisnormally

distributed.

11) Testtheclaimthatσ2≥1.8ifn=15,s2=1.5,andα=0.05.Assumethatthepopulationisnormallydistributed.

12) Testtheclaimthatσ2≤28.8ifn=20,s2=55.8,andα=0.01.Assumethatthepopulationisnormally

distributed.

13) Testtheclaimthatσ2>17.1ifn=18,s2=24.3,andα=0.01.Assumethatthepopulationisnormally

distributed.

14) Testtheclaimthatσ2<50.4ifn=28,s2=31.5,andα=0.10.Assumethatthepopulationisnormally

distributed.

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15) Testtheclaimthatσ2≠54.4ifn=10,s2=60,andα=0.01.Assumethatthepopulationisnormallydistributed.

16) Testtheclaimthatσ=18.63ifn=12,s=17.1

andα =0.05.Assumethatthepopulationisnormally

distributed.

17) Testtheclaimthatσ≥9.38ifn=15,s=8.54

andα =0.05.Assumethatthepopulationisnormallydistributed.

18) Testtheclaimthatσ≤5.37ifn=20,s=7.47

andα =0.01.Assumethatthepopulationisnormallydistributed.

19) Testtheclaimthatσ>12.42ifn=18,s=14.76

andα =0.01.Assumethatthepopulationisnormally

distributed.

20) Testtheclaimthatσ<9.48ifn=28,s=7.48 andα =0.10.Assumethatthepopulationisnormallydistributed.

21) Testtheclaimthatσ≠20.88ifn=10,s=21.92

andα =0.01.Assumethatthepopulationisnormally

distributed.

22) ListedbelowaretheAprilutilitybills(indollars)foroneneighborhood.Assumingthatthedataisnormally

distributed,testtheclaimthatthestandarddeviationforthedatais$15.Useα

=0.01.

70 48 41 68 69 55 70 57 60 83

32 60 72 58

23) Thecommutetimes(inminutes)of20randomlyselectedadultmalesarelistedbelow.Testtheclaimthatthe

varianceislessthan6.25.Useα=0.05.Assumethepopulationisnormallydistributed.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

24) Ashippingfirmsuspectsthatthevarianceforacertainbrandoftireusedbyitstrucksisgreaterthan1,000,000.

Tochecktheclaim,thefirmputs101ofthesetiresonitstrucksandgetsastandarddeviationof1200miles.At

α=0.05,testtheshippingfirmʹsclaim.

25) Abrokeragefirmneedsinformationconcerningthestandarddeviationoftheaccountbalancesofitscustomers.

Frompreviousinformationitwasassumedtobe$250.Arandomsampleof61accountswaschecked.The

standarddeviationwas$286.20.Atα=0.01,testthefirmʹsassumption.Assumethattheaccountbalancesare

normallydistributed.

26) Inonearea,monthlyincomesoftechnologyrelatedworkershaveastandarddeviationof$650.Itisbelieved

thatthestandarddeviationofmonthlyincomesofnon–technologyworkersishigher.Asampleof71

non–technologyworkersarerandomlyselectedandfoundtohaveastandarddeviationof$950.Testtheclaim

thatnon–technologyworkershaveahigherstandarddeviation.Useα

=0.05.

27) Astatisticsprofessoratanall–menʹscollegedeterminedthatthestandarddeviationofmenʹsheightsis2.5

inches.Theprofessorthenrandomlyselected41femalestudentsfromanearbyall–femalecollegeandfound

thestandarddeviationtobe2.9inches.Testtheprofessorʹsclaimthatthestandarddeviationoffemaleheights

isgreaterthan2.5inches.Useα=0.01.

28) Anewgun–likeapparatushasbeendevisedtoreplacetheneedleinadministeringvaccines.Theapparatus,

whichisconnectedtoalargesupplyofvaccine,canbesettoinjectdifferentamountsoftheserum,butthe

varianceintheamountofseruminjectedtoagivenpersonmustnotbegreaterthan0.0 8toensureproper

inoculation.Arandomsampleof25injectionswasmeasured.SupposetheP–valueforthetestisp=0.0085.

Statetheproperconclusionusingα=0.01.

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10.5 PuttingItTogether:WhichMethodDoIUse?

1 Determinetheappropriatehypothesistesttoperform.

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

Provideanappropriateresponse.

1) In2010,36%ofadultsinacertaincountryweremorbidlyobese.Ahealthpractitionersuspectsthatthepercent

haschangedsincethen.Sheobtainsarandomsampleof1042adultsandfindsthat393aremorbidlyobese.Is

thissufficientevidencetosupportthepractitionerʹsclaimattheα=0.1levelofsignificance?Roundp

^tofive

decimalplaceswhencalculatingtheteststatistic.

2) In2010,themeanexpenditureforautoinsuranceinacertainstatewas$806.Aninsurancesalespersoninthis

statebelievesthatthemeanexpenditureforautoinsuranceislesstoday.Sheobtainsasimplerandomsample

of32autoinsurancepoliciesanddeterminesthemeanexpendituretobe$781withastandarddeviationof

$39.13.Isthereenoughevidencetosupporttheclaimthatthemeanexpenditureforautoinsuranceislessthan

the2010amountattheα=0.05levelofsignificance?

3) Apharmaceuticalcompanymanufacturesa81–mgpainreliever.Companyspecificationsincludethatthe

standarddeviationoftheamountoftheactiveingredientmustnotexceed2mg.Thequality –controlmanager

selectsarandomsampleof30tabletsfromacertainbatchandfindsthatthestandarddeviationis2.4mg.

Assumethattheamountoftheactiveingredientisnormallydistributed.Testtheclaimthatthestandard

deviationoftheamountoftheactiveingredientisgreaterthan2mgattheα=0.05levelofsignificance.

4) In2010,themeanforthenumberofpetsownedperhouseholdwas1.9.Apollof1023householdsconducted

thisyearreportedthemeanforthenumberofpetsownedperhouseholdtobe1.8.Assumingσ=1.1,isthere

sufficientevidencetosupporttheclaimthatthemeannumberofpetsownedhaschangedsince2010attheα =

0.1levelofsignificance?

10.6 TheProbabilityofaTypeIIErrorandthePoweroftheTest

1 DeterminetheprobabilityofmakingaTypeIIerrorandcomputethepowerofthetest.

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

Provideanappropriateresponse.

1) ItisdesiredtotestH0:μ=40againstH1:μ <40 usingα =0.10.Thepopulationinquestionisuniformly

distributedwithastandarddeviationof10.Arandomsampleof36willbedrawnfromthispopulation.Ifμis

reallyequalto35,whatistheprobabilitythatthehypothesistestwouldleadtheinvestigatortocommitaType

IIerror?

A) 0.0427 B) 0.9573 C) 0.4573 D) 0.0854

2) ItisdesiredtotestH0:μ=12againstH1:μ ≠12 usingα =0.05.Thepopulationinquestionisuniformly

distributedwithastandarddeviationof2.0.Arandomsampleof100willbedrawnfromthispopulation.Ifμ

isreallyequalto11.9,whatisthevalueofβassociatedwiththistest?

A) 0.0790 B) 0.9210 C) 0.4210 D) 0.0395

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

3) IthasbeenestimatedthattheG–carobtainsameanof40 milespergallononthehighway,andthecompany

thatmanufacturesthecarclaimsthatitexceedsthisestimateinhighwaydriving.Tosupportitsassertion,the

companyrandomlyselects36G–carsandrecordsthemileageobtainedforeachcaroveradrivingcourse

similartothatusedtoobtaintheestimate.Thefollowingdataresulted:x=41.5milespergallon,s=6milesper

gallon.Calculatethevalueofβifthetruevalueofthemeanisreally42milespergallon.Useα=0.025.

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

4) TheprobabilityofmakingaTypeIIerrorisindicatedbytheletter

A) βB) αC) μD) σ

5) ATypeIIerrorisanerrorthat

A) failstorejectH0

giventhatH1istrue. B) rejectsH0

giventhatH1isfalse.

C) failstorejectH0

giventhatH1isfalse. D) rejectsH0

giventhatH1istrue.

6) Inahypothesistestasthepopulationmeangetsclosertothehypothesizedmean,β

A) increases. B) decreases.

C) doesnotchange. D)

ecomesthereciprocalofα.

7) Thepowerofthetestis

A) 1–β.B)α.C)β.D)1–α.

8) Thegreaterthepowerofthetestthemorelikelythetestwill

A) rejectH0whenH1istrue. B) rejectH0whenH1isfalse.

C) failtorejectH0whenH1istrue. D) failtorejectH0whenH1isfalse.

9) Ifβiscomputedtobe0.763,thenthepowerofthetestis

A) 0.237. B) 0.763. C) 0.263. D) 0.737.

10) Apowercurveisagraphicthatplots

A) thepowerofthetestagainstvaluesofthepopulationmeanthatmakeH0false.

B) thepowerofthetestagainstvaluesofthepopulationmeanthatmakeH0true.

C) thepowerofthetestagainstvaluesofthehypothesizedmeanthatmakeH0false.

D) thepowerofthetestagainstvaluesofthehypothesizedmeanthatmakeH0true.

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Ch.10 HypothesisTestsRegardingaParameter

AnswerKey

10.1 TheLanguageofHypothesisTesting

1 Determinethenullandalternativehypotheses.

2 ExplainTypeIandTypeIIerrors.

3 Stateconclusionstohypothesistests.

10.2 HypothesisTestsforaPopulationProportio

1 Explainthelogicofhypothesistesting.

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2 Testhypothesesaboutapopulationproportion.

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3 Testhypothesesaboutapopulationproportionusingthebinomialprobabilitydistribution.

10.3 HypothesisTestsforaPopulationMean

1 Testhypothesesaboutamean.

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2 Understandthedifferencebetweenstatisticalsignificanceandpracticalsignificance.

10.4 HypothesisTestsforaPopulationStandardDeviatio

1 Testhypothesesaboutapopulationstandarddeviation.

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10.5 PuttingItTogether:WhichMethodDoIUse?

1 Determinetheappropriatehypothesistesttoperform.

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10.6 TheProbabilityofaTypeIIErrorandthePoweroftheTest

1 DeterminetheprobabilityofmakingaTypeIIerrorandcomputethepowerofthetest.

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