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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.)
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.)
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.)
waitedmorethan3days?
A. 0.5174
B. 0.0174
C. 0.7500
D. 0.2143
Thenextﬁveproblemsrefertothefollowingstudy:Twentypercentofthestudentsatalocalcommunity
collegeliveinwithinﬁvemilesofthecampus.Thirtypercentofthestudentsatthesamecommunitycollege
kindofﬁnancialaid.
Exercise8.10.10
(Solutiononp.375.)
Findtheprobabilitythatarandomlychosenstudentatthelocalcommunitycollegedoesnotlive
withinﬁvemilesofthecampus.
A. 80%
B. 20%
C. 30%
D. Cannotbedetermined
Exercise8.10.11
(Solutiononp.375.)
Findtheprobabilitythatarandomlychosenstudentatthelocalcommunitycollegeliveswithin
A. 50%
B. 35%
C. 27.5%
D. 75%
Exercise8.10.12
(Solutiononp.375.)
Basedupontheaboveinformation,arelivinginstudenthousingwithinﬁvemilesofthecampus
andreceivingsomekindofﬁnancialaidmutuallyexclusive?
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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.)
college.
 1stquartile=\$250
 2ndquartile=\$700
 3rdquartile=\$1200
(These amountsarefor theschoolyear.) ) Ifasampleof200studentsistaken, , how manyare
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)
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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
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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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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