411
Exercise9.16.27
(Solutiononp.426.)
TheCravenbyMarkSalangsang
AvailableforfreeatConnexions<http://cnx.org/content/col10522/1.40>
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412
CHAPTER9. HYPOTHESISTESTING:SINGLEMEANANDSINGLE
PROPORTION
Exercise9.16.28
Toastmasters International cites a report t by y Gallop Poll that 40% % of f Americans fear r public
speaking. Astudentbelievesthatlessthan40%ofstudentsatherschoolfearpublicspeaking.
She randomly surveys 361 schoolmates and d finds that 135 report t they fear public c speaking.
Conductahypothesistestto determine ifthe percent at herschoolislessthan40%. . (Source:
http://toastmasters.org/artisan/detail.asp?CategoryID=1&SubCategoryID=10&ArticleID=429&Page=1
17
)
Exercise9.16.29
(Solutiononp.426.)
68%ofonlinecoursestaughtatcommunitycollegesnationwideweretaughtbyfull-timefaculty.
Totestif68%alsorepresentsCalifornia’spercentforfull-timefacultyteachingtheonlineclasses,
LongBeachCityCollege(LBCC),CA,wasrandomlyselectedforcomparison.Inthesameyear,34
ofthe44onlinecoursesLBCCofferedweretaughtbyfull-timefaculty.Conductahypothesistest
todetermineif68%representsCA.NOTE:Formoreaccurateresults,usemoreCAcommunity
collegesandthispastyear’sdata. (Sources: GrowingbyDegreesbyAllenandSeaman;Amit
Schitai,DirectorofInstructionalTechnologyandDistanceLearning,LBCC).
Exercise9.16.30
AccordingtoanarticleinBloombergBusinessweek,NewYorkCity’smostrecentadultsmoking
rateis14%.Supposethatasurveyisconductedtodeterminethisyear’srate. Nineoutof70ran-
domlychosenN.Y.Cityresidentsreplythattheysmoke.Conductahypothesistesttodetermineif
therateisstill14%orifithasdecreased.(Source: http://www.businessweek.com/news/2011-
09-15/nyc-smoking-rate-falls-to-record-low-of-14-bloomberg-says.html
18
)
Exercise9.16.31
(Solutiononp.426.)
ThemeanageofDeAnzaCollegestudentsinaprevioustermwas26.6yearsold.Aninstructor
thinksthemeanageforonlinestudentsisolderthan26.6. Sherandomlysurveys56onlinestu-
dentsandfindsthatthesamplemeanis29.4withastandarddeviationof2.1.Conductahypoth-
esistest.(Source: http://research.fhda.edu/factbook/DAdemofs/Fact_sheet_da_2006w.pdf
19
)
Exercise9.16.32
Registered nursesearned anaverage annualsalaryof$69,110. . For r that sameyear, asurvey
wasconductedof41Californiaregisterednursestodetermineiftheannualsalaryishigherthan
$69,110forCalifornianurses.Thesampleaveragewas$71,121withasamplestandarddeviationof
$7,489.Conductahypothesistest.(Source: http://www.bls.gov/oes/current/oes291111.htm
20
)
Exercise9.16.33
(Solutiononp.426.)
LaLecheLeagueInternationalreportsthatthemeanageofweaningachildfrombreastfeeding
isage4to5worldwide. InAmerica, , mostnursingmothersweantheirchildrenmuchearlier.
17http://toastmasters.org/artisan/detail.asp?CategoryID=1&SubCategoryID=10&ArticleID=429&Page=1
18
http://www.businessweek.com/news/2011-09-15/nyc-smoking-rate-falls-to-record-low-of-14-bloomberg-says.html
19
http://research.fhda.edu/factbook/DAdemofs/Fact_sheet_da_2006w.pdf
20
http://www.bls.gov/oes/current/oes291111.htm
AvailableforfreeatConnexions<http://cnx.org/content/col10522/1.40>
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413
Supposearandomsurveyisconductedof21U.S.motherswhorecentlyweanedtheirchildren.
Themeanweaningagewas9months(3/4year)withastandarddeviationof4months.Conduct
ahypothesistesttodetermineifthemeanweaningageintheU.S.islessthan4yearsold.(Source:
http://www.lalecheleague.org/Law/BAFeb01.html
21
)
9.16.1Trythesemultiplechoicequestions.
Exercise9.16.34
(Solutiononp.426.)
Whenanewdrugiscreated,thepharmaceuticalcompanymustsubjectittotestingbeforereceiv-
ingthenecessarypermissionfromtheFoodandDrugAdministration(FDA)tomarketthedrug.
Supposethenullhypothesisis“thedrugisunsafe.”WhatistheTypeIIError?
A. Toconcludethedrugissafewhenin,fact,itisunsafe
B. Tonotconcludethedrugissafewhen,infact,itissafe.
C. Toconcludethedrugissafewhen,infact,itissafe.
D. Tonotconcludethedrugisunsafewhen,infact,itisunsafe
Thenexttwoquestionsrefertothefollowinginformation: Over thepast fewdecades,publichealth
officialshaveexaminedthelinkbetweenweightconcernsandteengirlssmoking.Researcherssurveyeda
groupof273randomlyselectedteengirlslivinginMassachusetts(between12and15yearsold).Afterfour
yearsthegirlsweresurveyedagain.Sixty-three(63)saidtheysmokedtostaythin.Istheregoodevidence
thatmorethanthirtypercentoftheteengirlssmoketostaythin?
Exercise9.16.35
(Solutiononp.426.)
Thealternatehypothesisis
A. p<0.30
B. p0.30
C. p0.30
D. p>0.30
Exercise9.16.36
(Solutiononp.426.)
Afterconductingthetest,yourdecisionandconclusionare
A. RejectH
o
: Thereissufficientevidencetoconcludethatmorethan30%ofteengirlssmoketo
staythin.
B. Donotreject H
o
: Thereisnotsufficientevidencetoconcludethatlessthan30%ofteengirls
smoketostaythin.
C. DonotrejectH
o
: Thereisnotsufficientevidencetoconcludethatmorethan30%ofteengirls
smoketostaythin.
D. Reject H
o
: Thereissufficientevidencetoconcludethatlessthan30%ofteengirlssmoketo
staythin.
Thenextthreequestionsrefertothefollowinginformation: Astatisticsinstructorbelievesthatfewer
than20%ofEvergreenValleyCollege(EVC)studentsattendedtheopeningnightmidnightshowingof
thelatestHarryPottermovie. Shesurveys84ofherstudentsandfindsthat11ofattendedthemidnight
showing.
Exercise9.16.37
(Solutiononp.427.)
Anappropriatealternativehypothesisis
21
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414
CHAPTER9. HYPOTHESISTESTING:SINGLEMEANANDSINGLE
PROPORTION
A. p=0.20
B. p>0.20
C. p<0.20
D. p0.20
Exercise9.16.38
(Solutiononp.427.)
Ata1%levelofsignificance,anappropriateconclusionis:
A. ThereisinsufficientevidencetoconcludethatthepercentofEVCstudentsthatattendedthe
midnightshowingofHarryPotterislessthan20%.
B. Thereissufficient evidence toconclude that thepercentofEVCstudentsthatattendedthe
midnightshowingofHarryPotterismorethan20%.
C. There issufficientevidencetoconcludethatthepercentofEVCstudentsthatattendedthe
midnightshowingofHarryPotterislessthan20%.
D. ThereisinsufficientevidencetoconcludethatthepercentofEVCstudentsthatattendedthe
midnightshowingofHarryPotterisatleast20%.
Exercise9.16.39
(Solutiononp.427.)
TheTypeIerroristoconcludethatthepercentofEVCstudentswhoattendedis
A. atleast20%,wheninfact,itislessthan20%.
B. 20%,wheninfact,itis20%.
C. lessthan20%,wheninfact,itisatleast20%.
D. lessthan20%,wheninfact,itislessthan20%.
Thenexttwoquestionsrefertothefollowinginformation:
ItisbelievedthatLakeTahoeCommunityCollege(LTCC)IntermediateAlgebrastudentsgetlessthan7
hoursofsleeppernight,onaverage. Asurveyof22LTCCIntermediateAlgebrastudentsgenerateda
meanof7.24hourswithastandarddeviationof1.93hours. Atalevelofsignificance e of5%, doLTCC
IntermediateAlgebrastudentsgetlessthan7hoursofsleeppernight,onaverage?
Exercise9.16.40
(Solutiononp.427.)
Thedistributiontobeusedforthistestis
X
A. N
7.24,
1.93
p
22
B. N(7.24,1.93)
C. t
22
D. t
21
Exercise9.16.41
(Solutiononp.427.)
TheTypeIIerroristonotrejectthatthemeannumberofhoursofsleepLTCCstudentsgetper
nightisatleast7when,infact,themeannumberofhours
A. ismorethan7hours.
B. isatmost7hours.
C. isatleast7hours.
D. islessthan7hours.
Thenextthreequestionsrefertothefollowinginformation: Previously,anorganizationreportedthat
teenagersspent4.5hoursperweek,onaverage, onthephone. . Theorganizationthinksthat,currently,
themeanishigher. Fifteen(15)randomlychosenteenagerswereaskedhowmanyhoursperweekthey
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415
spendonthephone.Thesamplemeanwas4.75hourswithasamplestandarddeviationof2.0.Conducta
hypothesistest.
Exercise9.16.42
(Solutiononp.427.)
Thenullandalternatehypothesesare:
A. H
o
:
x=4.5,H
a
:
x>4.5
B. H
o
:m4.5H
a
:m<4.5
C. H
o
:m=4.75H
a:
m>4.75
D. H
o
:m=4.5H
a
:m>4.5
Exercise9.16.43
(Solutiononp.427.)
Atasignificancelevelofa=0.05,whatisthecorrectconclusion?
A. Thereisenoughevidencetoconcludethatthemeannumberofhoursismorethan4.75
B. Thereisenoughevidencetoconcludethatthemeannumberofhoursismorethan4.5
C. Thereisnotenoughevidencetoconcludethatthemeannumberofhoursismorethan4.5
D. Thereisnotenoughevidencetoconcludethatthemeannumberofhoursismorethan4.75
Exercise9.16.44
(Solutiononp.427.)
TheTypeIerroris:
A. Toconcludethatthecurrentmeanhoursperweekishigherthan4.5,wheninfact,itishigher.
B. Toconcludethatthecurrentmeanhoursperweekishigherthan4.5, wheninfact,itisthe
same.
C. Toconcludethatthemeanhoursperweekcurrentlyis4.5,wheninfact,itishigher.
D. Toconcludethatthemeanhoursperweekcurrentlyisnohigherthan4.5,wheninfact,itis
nothigher.
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416
CHAPTER9. HYPOTHESISTESTING:SINGLEMEANANDSINGLE
PROPORTION
9.17Review
22
Exercise9.17.1
(Solutiononp.427.)
RebeccaandMattare14yearoldtwins. Matt’sheightis2standarddeviationsbelowthemean
for14yearoldboys’height. Rebecca’sheightis0.10standarddeviationsabovethemeanfor14
yearoldgirls’height.Interpretthis.
A. Mattis2.1inchesshorterthanRebecca
B. Rebeccaisverytallcomparedtoother14yearoldgirls.
C. RebeccaistallerthanMatt.
D. Mattisshorterthantheaverage14yearoldboy.
Exercise9.17.2
(Solutiononp.427.)
ConstructahistogramoftheIPOdata(seeTableofContents,14. Appendix,DataSets). . Use5
intervals.
Thenextthreeexercisesrefertothefollowinginformation:Ninetyhomeownerswereaskedthenumber
ofestimatestheyobtainedbeforehavingtheirhomesfumigated.X=thenumberofestimates.
x
Rel.Freq.
CumulativeRel.Freq.
1
0.3
2
0.2
4
0.4
5
0.1
Table9.5
Completethecumulativerelativefrequencycolumn.
Exercise9.17.3
(Solutiononp.427.)
Calculatethesamplemean(a),thesamplestandarddeviation(b)andthepercentoftheestimates
thatfallatorbelow4(c).
Exercise9.17.4
(Solutiononp.427.)
Calculatethemedian,M,thefirstquartile,Q1,thethirdquartile,Q3.Thenconstructaboxplotof
thedata.
Exercise9.17.5
(Solutiononp.427.)
Themiddle50%ofthedataarebetween_____and_____.
Thenextthreequestionsrefertothefollowingtable:Seventy5thand6thgraderswereaskedtheirfavorite
dinner.
Pizza
Hamburgers
Spaghetti
Friedshrimp
5thgrader
15
6
9
0
6thgrader
15
7
10
8
Table9.6
Exercise9.17.6
(Solutiononp.427.)
Findtheprobabilitythatonerandomlychosenchildisinthe6thgradeandprefersfriedshrimp.
22
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417
A.
32
70
B.
8
32
C.
8
8
D.
8
70
Exercise9.17.7
(Solutiononp.427.)
Findtheprobabilitythatachilddoesnotpreferpizza.
A.
30
70
B.
30
40
C.
40
70
D. 1
Exercise9.17.8
(Solutiononp.427.)
Findtheprobabilityachildisinthe5thgradegiventhatthechildprefersspaghetti.
A.
9
19
B.
9
70
C.
9
30
D.
19
70
Exercise9.17.9
(Solutiononp.427.)
Asampleofconvenienceisarandomsample.
A. true
B. false
Exercise9.17.10
(Solutiononp.427.)
Astatisticisanumberthatisapropertyofthepopulation.
A. true
B. false
Exercise9.17.11
(Solutiononp.427.)
Youshouldalwaysthrowoutanydatathatareoutliers.
A. true
B. false
Exercise9.17.12
(Solutiononp.427.)
LeebakespiesforasmallrestaurantinFelton,CA.Shegenerallybakes20piesinaday,onthe
average.Ofinterestisthenum.berofpiesshebakeseachday
a. DefinetheRandomVariableX.
b. StatethedistributionforX.
c. FindtheprobabilitythatLeebakesmorethan25piesinanygivenday.
Exercise9.17.13
(Solutiononp.428.)
SixdifferentbrandsofItaliansaladdressingwererandomlyselectedatasupermarket.Thegrams
offatperservingare7,7,9,6,8,5.Assumethattheunderlyingdistributionisnormal.Calculatea
95%confidenceintervalforthepopulationmeangramsoffatperservingofItaliansaladdressing
soldinsupermarkets.
Exercise9.17.14
(Solutiononp.428.)
Given:uniform,exponential,normaldistributions.Matcheachtoastatementbelow.
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418
CHAPTER9. HYPOTHESISTESTING:SINGLEMEANANDSINGLE
PROPORTION
a. mean=median6=mode
b. mean>median>mode
c. mean=median=mode
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419
9.18Lab:HypothesisTestingofaSingleMeanandSingleProportion
23
ClassTime:
Names:
9.18.1StudentLearningOutcomes:
 Thestudentwillselecttheappropriatedistributionstouseineachcase.
 Thestudentwillconducthypothesistestsandinterprettheresults.
9.18.2TelevisionSurvey
Inarecentsurvey,itwasstatedthatAmericanswatchtelevisiononaveragefourhoursperday. Assume
that2. Usingyourclassasthesample, , conduct ahypothesistestto determine ifthe averagefor
studentsatyourschoolislower.
1. H
o
:
2. H
a
:
3. Inwords,definetherandomvariable.__________=
4. Thedistributiontouseforthetestis:
5. Determinetheteststatisticusingyourdata.
6. Drawagraphandlabelitappropriately.Shadetheactuallevelofsignificance.
a. Graph:
23
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420
CHAPTER9. HYPOTHESISTESTING:SINGLEMEANANDSINGLE
PROPORTION
Figure9.9
b. Determinethep-value:
7. Doyouordoyounotrejectthenullhypothesis?Why?
8. Writeaclearconclusionusingacompletesentence.
9.18.3LanguageSurvey
About42.3%ofCaliforniansand19.6%ofallAmericansoverage5speakalanguageotherthanEnglish
athome. Usingyour r classasthe sample, conduct ahypothesistesttodetermine ifthe percent ofthe
studentsatyourschoolthatspeakalanguageotherthanEnglishathomeisdifferentfrom42.3%.(Source:
http://www.census.gov/hhes/socdemo/language/
24
)
1. H
o
:
2. H
a
:
3. Inwords,definetherandomvariable.__________=
4. Thedistributiontouseforthetestis:
5. Determinetheteststatisticusingyourdata.
6. Drawagraphandlabelitappropriately.Shadetheactuallevelofsignificance.
24
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