361
8.10Review
11
Thenextthreeproblemsrefertothefollowingsituation:Supposethatasampleof15randomlychosen
peoplewereputonaspecialweightlossdiet.Theamountofweightlost,inpounds,followsanunknown
distributionwithmeanequalto12poundsandstandarddeviationequalto3pounds. Assumethatthe
distributionfortheweightlossisnormal.
Exercise8.10.1
(Solutiononp.375.)
To findthe probabilitythatthe meanamountofweightlost by15people isno morethan14
pounds,therandomvariableshouldbe:
A. Thenumberofpeoplewholostweightonthespecialweightlossdiet
B. Thenumberofpeoplewhowereonthediet
C. Themeanamountofweightlostby15peopleonthespecialweightlossdiet
D. Thetotalamountofweightlostby15peopleonthespecialweightlossdiet
Exercise8.10.2
(Solutiononp.375.)
Findtheprobabilityaskedforinthepreviousproblem.
Exercise8.10.3
(Solutiononp.375.)
Findthe90thpercentileforthemeanamountofweightlostby15people.
Thenextthreequestionsrefertothefollowingsituation: Thetime ofoccurrenceofthefirstaccident
duringrush-hourtrafficatamajorintersectionisuniformlydistributedbetweenthethreehourinterval4
p.m.to7p.m.LetX=theamountoftime(hours)ittakesforthefirstaccidenttooccur.
 So,ifanaccidentoccursat4p.m.,theamountoftime,inhours,ittookfortheaccidenttooccuris
_______.
 m=_______
 s=_______
Exercise8.10.4
(Solutiononp.375.)
Whatistheprobabilitythatthetimeofoccurrenceiswithinthefirsthalf-hourorthelasthourof
theperiodfrom4to7p.m.?
A. Cannotbedeterminedfromtheinformationgiven
B.
1
6
C.
1
2
D.
1
3
Exercise8.10.5
(Solutiononp.375.)
The20thpercentileoccursafterhowmanyhours?
A. 0.20
B. 0.60
C. 0.50
D. 1
Exercise8.10.6
(Solutiononp.375.)
AssumeRamonhaskepttrackofthetimesforthefirstaccidentstooccurfor40differentdays.Let
C=thetotalcumulativetime.ThenCfollowswhichdistribution?
A. U(0,3)
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362
CHAPTER8. CONFIDENCEINTERVALS
B. Exp
1
3
C. N(60,5.477)
D. N(1.5,0.01875)
Exercise8.10.7
(Solutiononp.375.)
Usingtheinformationinquestion#6,findtheprobabilitythatthetotaltimeforallfirstaccidents
tooccurismorethan43hours.
Thenexttwoquestionsrefertothefollowingsituation: Thelengthoftimeaparentmustwaitforhis
childrentocleantheirroomsisuniformlydistributedinthetimeintervalfrom1to15days.
Exercise8.10.8
(Solutiononp.375.)
Howlongmustaparentexpecttowaitforhischildrentocleantheirrooms?
A. 8days
B. 3days
C. 14days
D. 6days
Exercise8.10.9
(Solutiononp.375.)
Whatistheprobabilitythataparentwillwaitmorethan6daysgiventhattheparenthasalready
waitedmorethan3days?
A. 0.5174
B. 0.0174
C. 0.7500
D. 0.2143
Thenextfiveproblemsrefertothefollowingstudy:Twentypercentofthestudentsatalocalcommunity
collegeliveinwithinfivemilesofthecampus.Thirtypercentofthestudentsatthesamecommunitycollege
receivesomekindoffinancialaid. Ofthosewholivewithinfivemilesofthecampus,75%receivesome
kindoffinancialaid.
Exercise8.10.10
(Solutiononp.375.)
Findtheprobabilitythatarandomlychosenstudentatthelocalcommunitycollegedoesnotlive
withinfivemilesofthecampus.
A. 80%
B. 20%
C. 30%
D. Cannotbedetermined
Exercise8.10.11
(Solutiononp.375.)
Findtheprobabilitythatarandomlychosenstudentatthelocalcommunitycollegeliveswithin
fivemilesofthecampusorreceivessomekindoffinancialaid.
A. 50%
B. 35%
C. 27.5%
D. 75%
Exercise8.10.12
(Solutiononp.375.)
Basedupontheaboveinformation,arelivinginstudenthousingwithinfivemilesofthecampus
andreceivingsomekindoffinancialaidmutuallyexclusive?
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363
A. Yes
B. No
C. Cannotbedetermined
Exercise8.10.13
(Solutiononp.375.)
Theinterestratechargedonthefinancialaidis_______data.
A. quantitativediscrete
B. quantitativecontinuous
C. qualitativediscrete
D. qualitative
Exercise8.10.14
(Solutiononp.375.)
Whatfollowsisinformationaboutthestudentswhoreceivefinancialaidatthelocalcommunity
college.
 1stquartile=$250
 2ndquartile=$700
 3rdquartile=$1200
(These amountsarefor theschoolyear.) ) Ifasampleof200studentsistaken, , how manyare
expectedtoreceive$250ormore?
A. 50
B. 250
C. 150
D. Cannotbedetermined
Thenexttwoproblemsrefertothefollowinginformation: P(A) = 0.2,P(B) = 0.3, AandBare
independentevents.
Exercise8.10.15
(Solutiononp.375.)
P(AANDB)=
A. 0.5
B. 0.6
C. 0
D. 0.06
Exercise8.10.16
(Solutiononp.375.)
P(AORB)=
A. 0.56
B. 0.5
C. 0.44
D. 1
Exercise8.10.17
(Solutiononp.375.)
IfHandDaremutuallyexclusiveevents, P(H)=0.25,P(D)=0.15,thenP(HjD)
A. 1
B. 0
C. 0.40
D. 0.0375
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364
CHAPTER8. CONFIDENCEINTERVALS
8.11Lab1:ConfidenceInterval(HomeCosts)
12
ClassTime:
Names:
8.11.1StudentLearningOutcomes:
 Thestudentwillcalculatethe90%confidenceintervalforthemeancostofahomeintheareainwhich
thisschoolislocated.
 Thestudentwillinterpretconfidenceintervals.
 Thestudentwilldeterminetheeffectsthatchangingconditionshasontheconfidenceinterval.
8.11.2CollecttheData
ChecktheRealEstatesectioninyourlocalnewspaper. (Note: : manypapersonlylistthemonedayper
week.Also,wewillassumethathomescomeupforsalerandomly.)Recordthesalespricesfor35randomly
selectedhomesrecentlylistedinthecounty.
1. Completethetable:
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
Table8.2
8.11.3DescribetheData
1. Computethefollowing:
a.
x=
b. s
x
=
c. n=
2. DefinetheRandomVariable
X,inwords.
X=
3. Statetheestimateddistributiontouse.Usebothwordsandsymbols.
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365
8.11.4FindtheConfidenceInterval
1. Calculatetheconfidenceintervalandtheerrorbound.
a. ConfidenceInterval:
b. ErrorBound:
2. Howmuchareaisinbothtails(combined)?a=
3. Howmuchareaisineachtail?
a
2
=
4. Fillintheblanksonthegraphwiththeareaineachsection. . Then,fillinthenumberlinewiththe
upperandlowerlimitsoftheconfidenceintervalandthesamplemean.
Figure8.5
5. Somestudentsthinkthata90%confidenceintervalcontains90%ofthedata. . Usethelistofdataon
thefirstpageandcounthowmanyofthedatavaluesliewithintheconfidenceinterval.Whatpercent
isthis?Isthispercentcloseto90%?Explainwhythispercentshouldorshouldnotbecloseto90%.
8.11.5DescribetheConfidenceInterval
1. Intwotothreecompletesentences,explainwhataConfidenceIntervalmeans(ingeneral),asifyou
weretalkingtosomeonewhohasnottakenstatistics.
2. Inonetotwocompletesentences,explainwhatthisConfidenceIntervalmeansforthisparticular
study.
8.11.6UsetheDatatoConstructConfidenceIntervals
1. Using g the e above e information, , construct t a confidence e interval for r each confidence e level
given.
Confidencelevel
EBM/ErrorBound
ConfidenceInterval
50%
80%
95%
99%
Table8.3
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366
CHAPTER8. CONFIDENCEINTERVALS
2. WhathappenstotheEBMastheconfidencelevelincreases?Doesthewidthoftheconfidenceinterval
increaseordecrease?Explainwhythishappens.
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367
8.12Lab2:ConfidenceInterval(PlaceofBirth)
13
ClassTime:
Names:
8.12.1StudentLearningOutcomes:
 Thestudentwillcalculatethe90%confidenceintervalforproportionofstudentsinthisschoolthat
wereborninthisstate.
 Thestudentwillinterpretconfidenceintervals.
 Thestudentwilldeterminetheeffectsthatchangingconditionshaveontheconfidenceinterval.
8.12.2CollecttheData
1. Surveythestudentsinyourclass,askingthemiftheywereborninthisstate.LetX=thenumberthat
wereborninthisstate.
a. n=____________
b. x=____________
2. DefinetheRandomVariableP’inwords.
3. Statetheestimateddistributiontouse.
8.12.3FindtheConfidenceIntervalandErrorBound
1. Calculatetheconfidenceintervalandtheerrorbound.
a. ConfidenceInterval:
b. ErrorBound:
2. Howmuchareaisinbothtails(combined)?a=
3. Howmuchareaisineachtail?
a
2
=
4. Fillintheblanksonthegraphwiththeareaineachsection. . Then,fillinthenumberlinewiththe
upperandlowerlimitsoftheconfidenceintervalandthesampleproportion.
Figure8.6
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368
CHAPTER8. CONFIDENCEINTERVALS
8.12.4DescribetheConfidenceInterval
1. Intwotothreecompletesentences,explainwhataConfidenceIntervalmeans(ingeneral),asifyou
weretalkingtosomeonewhohasnottakenstatistics.
2. Inonetotwocompletesentences,explainwhatthisConfidenceIntervalmeansforthisparticular
study.
3. Using g the above information, , construct t a confidence interval l for r each h given n confidence level
given.
Confidencelevel
EBP/ErrorBound
ConfidenceInterval
50%
80%
95%
99%
Table8.4
4. WhathappenstotheEBPastheconfidencelevelincreases?Doesthewidthoftheconfidenceinterval
increaseordecrease?Explainwhythishappens.
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369
8.13Lab3:ConfidenceInterval(Womens’Heights)
14
ClassTime:
Names:
8.13.1StudentLearningOutcomes:
 Thestudentwillcalculatea90%confidenceintervalusingthegivendata.
 The studentwilldeterminethe relationshipbetweentheconfidence leveland thepercent ofcon-
structedintervalsthatcontainthepopulationmean.
8.13.2Given:
1. Heightsof100Women(inInches)
59.4
71.6
69.3
65.0
62.9
66.5
61.7
55.2
67.5
67.2
63.8
62.9
63.0
63.9
68.7
65.5
61.9
69.6
58.7
63.4
61.8
60.6
69.8
60.0
64.9
66.1
66.8
60.6
65.6
63.8
61.3
59.2
64.1
59.3
64.9
62.4
63.5
60.9
63.3
66.3
61.5
64.3
62.9
60.6
63.8
58.8
64.9
65.7
62.5
70.9
62.9
63.1
62.2
58.7
64.7
66.0
60.5
64.7
65.4
60.2
65.0
64.1
61.1
65.3
64.6
59.2
61.4
62.0
63.5
61.4
65.5
62.3
65.5
64.7
58.8
66.1
64.9
66.9
57.9
69.8
58.5
63.4
69.2
65.9
62.2
60.0
58.1
62.5
62.4
59.1
66.4
61.2
60.4
58.7
66.7
67.5
63.2
56.6
67.7
62.5
Table8.5
Listedabovearetheheightsof100women. Usearandomnumbergeneratortorandomlyselect10
datavalues.
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370
CHAPTER8. CONFIDENCEINTERVALS
2. Calculatethesamplemeanandsamplestandarddeviation. . Assumethatthepopulationstandard
deviationisknowntobe3.3inches. Withthesevalues,constructa90%confidenceintervalforyour
sampleof10values.Writetheconfidenceintervalyouobtainedinthefirstspaceofthetablebelow.
3. Nowwriteyourconfidenceintervalontheboard. . Asothersintheclasswritetheirconfidenceinter-
valsontheboard,copythemintothetablebelow:
90%ConfidenceIntervals
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
Table8.6
8.13.3DiscussionQuestions
1. Theactualpopulationmeanforthe100heightsgivenaboveism63.4. . Usingtheclasslistingof
confidenceintervals, counthowmanyofthemcontainthepopulationmeanm; i.e.,forhowmany
intervalsdoesthevalueofmliebetweentheendpointsoftheconfidenceinterval?
2. Dividethisnumberbythetotalnumberofconfidenceintervalsgeneratedbytheclasstodetermine
thepercentofconfidenceintervalsthatcontainsthemeanm.Writethispercentbelow.
3. Isthepercentofconfidenceintervalsthatcontainthepopulationmeanmcloseto90%?
4. Supposewehadgenerated100confidenceintervals.Whatdoyouthinkwouldhappentothepercent
ofconfidenceintervalsthatcontainedthepopulationmean?
5. Whenweconstructa90%confidenceinterval,wesaythatweare90%confidentthatthetruepopu-
lationmeanlieswithintheconfidenceinterval. Usingcompletesentences,explainwhatwemean
bythisphrase.
6. Somestudentsthinkthata90%confidenceintervalcontains90%ofthedata.Usethelistofdatagiven
(theheightsofwomen)andcounthowmanyofthedatavaluesliewithintheconfidenceintervalthat
yougeneratedonthatpage. Howmanyofthe100datavaluesliewithinyourconfidenceinterval?
Whatpercentisthis?Isthispercentcloseto90%?
7. Explainwhyitdoesnotmakesensetocountdatavaluesthatlieinaconfidenceinterval.Thinkabout
therandomvariablethatisbeingusedintheproblem.
8. Supposeyouobtainedtheheightsof10womenandcalculatedaconfidenceintervalfromthisinfor-
mation. Withoutknowingthepopulationmeanm,wouldyouhaveanywayofknowingforcertain
ifyourintervalactuallycontainedthevalueofm?Explain.
NOTE
:ThislabwasdesignedandcontributedbyDianeMathios.
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