TesttyBanktyFortyProbabilitytyAndtyStatisticstyFortyEngineeringtyAndtyThetySciencesty8thtyEdtybytyJaytyL.tyDevore.
Chapterty1ty–tyOverviewtyandtyDescriptivetyStatistics
SHORTtyANSWER
1. Givetyonetypossibletysampletyoftysizety4tyfromtyeachtyoftythetyfollowingtypopulations:
a. AlltydailytynewspaperstypublishedtyintythetyUnitedtyStates
b. AlltycompaniestylistedtyontythetyNewtyYorktyStocktyExchange
c. Alltystudentstyattyyourtycollegetyortyuniversity
d. Alltygradetypointtyaveragestyoftystudentstyattyyourtycollegetyortyuniversity
ANS:
a. HoustontyChronicle,tyDestyMoinestyRegister,tyChicagotyTribune,tyWashingtontyPost
b. CapitaltyOne,tyCampbelltySoup,tyMerrilltyLynch,tyPulitzer
c. JohntyAnderson,tyEmilytyBlack,tyBillt y Carter,tyKaytyDavis
d. 2.58.ty2.96,ty3.51,ty3.69
PTS:t y t y 1
2. AtySoutherntyStatetyUniversitytysystemtyconsiststyofty23tycampuses.tyAntyadministratortywishestytotymaketyantyinfere
ncetyabouttythetyaveragetydistancetybetweentythetyhometownstyoftystudentstyandtytheirtycampuses.tyDescribetyandtydis
cusstyseveraltydifferenttysamplingtymethodstythattymighttybetyemployed.tyWouldtythistybetyantyenumerativetyortyantya
nalytictystudy?tyExplaintyyourtyreasoning.
ANS:
OnetycouldtytaketyatysimpletyrandomtysampletyoftystudentstyfromtyalltystudentstyintythetyCaliforniatyStatetyUniversitytys
ystemtyandtyasktyeachtystudenttyintythetysampletytotyreporttythetydistancetyfromtytheirtyhometowntytotycampus.tyAltern
atively,tythetysampletycouldtybetygeneratedtybytytakingtyatystratifiedtyrandomtysampletybytytakingtyatysimpletyrandomty
sampletyfromtyeachtyoftythety23tycampusestyandtyagaintyaskingtyeachtystudenttyintythetysampletytotyreporttythetydistanc
etyfromtytheirtyhometowntytotycampus.
Certaintyproblemstymighttyarisetywithtyselftyreportingtyoftydistances,tysuchtyastyrecordingtyerrortyortypoortyrecall.tyThistystud
ytyistyenumerativetybecausetytheretyexiststyatyfinite,tyidentifiabletypopulationtyoftyobjectstyfromtywhichtytotysample.
PTS:t y t y 1
3. AtyMichigantycitytydividestynaturallytyintotytentydistricttyneighborhoods.tyHowtymighttyatyrealtyestatetyappraisertyselec
ttyatysampletyoftysingle-
familytyhomestythattycouldtybetyusedtyastyatybasistyfortydevelopingtyantyequationtytotypredicttyappraisedtyvaluetyfromt
ycharacteristicstysuchtyastyage,tysize,tynumbertyoftybathrooms,tyandtydistancetytotythetynearesttyschool,tyandtysotyon?t
y Istythetystudytyenumerativetyortyanalytic?
ANS:
Onetycouldtygeneratetyatysimpletyrandomtysampletyoftyalltysingletyfamilytyhomestyintythetycitytyortyatystratifiedtyrandom
tysampletybytytakingtyatysimpletyrandomtysampletyfromtyeachtyoftythety10tydistricttyneighborhoods.tyFromtyeachtyoftyth
etyhomestyintythetysampletythetynecessarytyvariablestywouldtybetycollected.tyThistywouldtybetyantyenumerativetystudyty
becausetytheretyexiststyatyfinite,tyidentifiabletypopulationtyoftyobjectstyfromtywhichtytotysample.
, PTS:t y t y 1
4. Antyexperimenttywastycarriedtyouttytotystudytyhowtyflowtyratetythroughtyatysolenoidtyvalvetyintyantyautomobile‘stypollu
tion-
controltysystemtydependedtyontythreetyfactors:t y armaturetylengths,tyspringtyload,tyandtybobbintydepth.t y Twotydiffere
nttylevelsty(lowtyandtyhigh)tyoftyeachtyfactortyweretychosen,tyandtyatysingletyobservationtyontyflowtywastymadetyfortyea
chtycombinationtyoftylevels.
a. Thetyresultingtydatatysettyconsistedtyoftyhowtymanytyobservations?
b. Istythistyantyenumerativetyortyanalytictystudy?tyExplaintyyourtyreasoning.
ANS:
a. Numbertyobservationstyequalty2tyty 2tyt y 2=8
b. Thistycouldtybetycalledtyantyanalytictystudytybecausetythetydatatywouldtybetycollectedtyontyantyexistin
gtyprocess.tyTheretyistynotysamplingtyframe.
PTS:t y t y 1
5. Thetyaccompanyingtydatatyspecifictygravitytyvaluestyfortyvarioustywoodtytypestyusedtyintyconstructionty.
.41 .41 .42 .42. .42 .42 .42 .43 .44
.54 .55 .58 .62 .66 .66 .67 .68 .75
.31 .35 .36 .36 .37 .38 .40 .40 .40
.45 .46 .46 .47 .48 .48 .48 .51 .54
Constructtyatystem-and-leaftydisplaytyusingtyrepeatedtystemstyandtycommenttyontyanytyinterestingtyfeaturestyoftythetydisplay.
ANS:
OnetymethodtyoftydenotingtythetypairstyoftystemstyhavingtyequaltyvaluestyistytotydenotetythetystemtybytyL,tyforty‗low‘tya
ndtythetysecondtystemtybytyH,tyforty‗high‘.t y Usingtythistynotation,tythetystem-and-
leaftydisplaytywouldtyappeartyastyfollows:
3L 1 stem:tytenths
3H 56678 leaf:t y hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
Thetystem-and-
leaftydisplaytyontythetyprevioustypagetyshowstythatty.45tyistyatygoodtyrepresentativetyvaluetyfortythetydata.t y Intyadditio
n,tythetydisplaytyistynottysymmetrictyandtyappearstytotybetypositivelytyskewed.t y Thetyspreadtyoftythetydatatyisty.75ty-
ty.31ty=ty.44,tywhichtyisty.44/.45ty=ty.978tyortyaboutty98%tyoftythetytypicaltyvaluetyofty.45.t y Thistyconstitutestyatyreaso
nablytylargetyamounttyoftyvariationtyintythetydata.t y Thetydatatyvaluety.75tyistyatypossibletyoutlier.
PTS:t y t y 1
6. Temperaturetytransducerstyoftyatycertaintytypetyaretyshippedtyintybatchestyofty50.t y Atysampletyofty60tybatchestywasty
selected,tyandtythetynumbertyoftytransducerstyintyeachtybatchtynottyconformingtytotydesigntyspecificationstywastydet
ermined,tyresultingtyintythetyfollowingtydata:
0 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
4t y t y 2t y t y
1t y t y 3
2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
1t y t y 2t y t y
4t y t y 0
,5 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
0t y t y 2t y t y
3t y t y 2
, a. Determinetyfrequenciestyandtyrelativetyfrequenciestyfortythetyobservedtyvaluestyoftyxty=tynumbertyof
nonconformingtytransducerstyintyatybatch.
b. Whattyproportiontyoftybatchestyintythetysampletyhastyattymosttyfourtynonconformingtytransducers?tyWhattyprop
ortiontyhastyfewertythantyfour?tyWhattyproportiontyhastyattyleasttyfourtynonconformingtyunits?
ANS:
a.
NumbertyNonconforming Frequency RelativetyFrequency
0 7 0.117
1 12 0.200
2 13 0.217
3 14 0.233
4 6 0.100
5 3 0.050
6 3 0.050
7 1 0.017
8 1 0.017
1.001
Thetyrelativet y frequenciestydon’ttyaddtyuptyexactlytytoty1becausetytheytyhavetybeentyrounded
b.tyThetynumbertyoftybatchestywithtyattymostty4tynonconformingtyitemstyisty7+12+13+14+6=52,tywhichtyistyatyproporti
ontyofty52/60=.867.tyThetyproportiontyoftybatchestywithty(strictly)tyfewertythanty4tynonconformingtyitemstyisty46/60
=.767.
PTS:t y t y 1
7. Thetynumbertyoftycontaminatingtyparticlestyontyatysilicontywafertypriortytotyatycertaintyrinsingtyprocesstywastydetermin
edtyfortyeachtywafertyintyatysampletysizety100,tyresultingtyintythetyfollowingtyfrequencies:
Numbertyoft y particles Frequency Numbertyoft y particles Frequency
0 1 8 12
1 2 9 4
2 3 10 5
3 12 11 3
4 11 12 1
5 15 13 2
6 18 14 1
7 10
a. Whattyproportiontyoftythetysampledtywaferstyhadtyattyleasttytwotyparticles?tyAttyleasttysixtyparticles?
b. Whattyproportiontyoftythetysampledtywaferstyhadtybetweentyfourtyandtyninetyparticles,tyinclusive?tyStrictlytybetwee
ntyfourtyandtyninetyparticles?
ANS:
a. Fromtythistyfrequencytydistribution,tythetyproportiontyoftywaferstythattycontainedtyattyleasttytwotyparticlestyisty(100-1-
2)/100ty=
.97,tyorty97%.tyIntyatysimilartyfashion,tythetyproportiontycontainingtyattyleastty6typarticlestyisty(100ty–ty1-2-3-12-
11-15)/100ty=ty56/100ty=ty.56,tyorty56%.
b. Thetyproportiontycontainingtybetweenty4tyandty9typarticlestyinclusivetyisty(11+15+18+10+12+4)/100ty=ty70/100t
y=ty.70,tyorty70%.tyThetyproportiontythattycontaintystrictlytybetweenty4tyandty9ty(meaningtystrictlytymoretythanty4ty
andtystrictlytylesstythanty9)tyisty(15+ty18+10+12)/100=ty55/100ty=ty.55,tyorty55%.
Chapterty1ty–tyOverviewtyandtyDescriptivetyStatistics
SHORTtyANSWER
1. Givetyonetypossibletysampletyoftysizety4tyfromtyeachtyoftythetyfollowingtypopulations:
a. AlltydailytynewspaperstypublishedtyintythetyUnitedtyStates
b. AlltycompaniestylistedtyontythetyNewtyYorktyStocktyExchange
c. Alltystudentstyattyyourtycollegetyortyuniversity
d. Alltygradetypointtyaveragestyoftystudentstyattyyourtycollegetyortyuniversity
ANS:
a. HoustontyChronicle,tyDestyMoinestyRegister,tyChicagotyTribune,tyWashingtontyPost
b. CapitaltyOne,tyCampbelltySoup,tyMerrilltyLynch,tyPulitzer
c. JohntyAnderson,tyEmilytyBlack,tyBillt y Carter,tyKaytyDavis
d. 2.58.ty2.96,ty3.51,ty3.69
PTS:t y t y 1
2. AtySoutherntyStatetyUniversitytysystemtyconsiststyofty23tycampuses.tyAntyadministratortywishestytotymaketyantyinfere
ncetyabouttythetyaveragetydistancetybetweentythetyhometownstyoftystudentstyandtytheirtycampuses.tyDescribetyandtydis
cusstyseveraltydifferenttysamplingtymethodstythattymighttybetyemployed.tyWouldtythistybetyantyenumerativetyortyantya
nalytictystudy?tyExplaintyyourtyreasoning.
ANS:
OnetycouldtytaketyatysimpletyrandomtysampletyoftystudentstyfromtyalltystudentstyintythetyCaliforniatyStatetyUniversitytys
ystemtyandtyasktyeachtystudenttyintythetysampletytotyreporttythetydistancetyfromtytheirtyhometowntytotycampus.tyAltern
atively,tythetysampletycouldtybetygeneratedtybytytakingtyatystratifiedtyrandomtysampletybytytakingtyatysimpletyrandomty
sampletyfromtyeachtyoftythety23tycampusestyandtyagaintyaskingtyeachtystudenttyintythetysampletytotyreporttythetydistanc
etyfromtytheirtyhometowntytotycampus.
Certaintyproblemstymighttyarisetywithtyselftyreportingtyoftydistances,tysuchtyastyrecordingtyerrortyortypoortyrecall.tyThistystud
ytyistyenumerativetybecausetytheretyexiststyatyfinite,tyidentifiabletypopulationtyoftyobjectstyfromtywhichtytotysample.
PTS:t y t y 1
3. AtyMichigantycitytydividestynaturallytyintotytentydistricttyneighborhoods.tyHowtymighttyatyrealtyestatetyappraisertyselec
ttyatysampletyoftysingle-
familytyhomestythattycouldtybetyusedtyastyatybasistyfortydevelopingtyantyequationtytotypredicttyappraisedtyvaluetyfromt
ycharacteristicstysuchtyastyage,tysize,tynumbertyoftybathrooms,tyandtydistancetytotythetynearesttyschool,tyandtysotyon?t
y Istythetystudytyenumerativetyortyanalytic?
ANS:
Onetycouldtygeneratetyatysimpletyrandomtysampletyoftyalltysingletyfamilytyhomestyintythetycitytyortyatystratifiedtyrandom
tysampletybytytakingtyatysimpletyrandomtysampletyfromtyeachtyoftythety10tydistricttyneighborhoods.tyFromtyeachtyoftyth
etyhomestyintythetysampletythetynecessarytyvariablestywouldtybetycollected.tyThistywouldtybetyantyenumerativetystudyty
becausetytheretyexiststyatyfinite,tyidentifiabletypopulationtyoftyobjectstyfromtywhichtytotysample.
, PTS:t y t y 1
4. Antyexperimenttywastycarriedtyouttytotystudytyhowtyflowtyratetythroughtyatysolenoidtyvalvetyintyantyautomobile‘stypollu
tion-
controltysystemtydependedtyontythreetyfactors:t y armaturetylengths,tyspringtyload,tyandtybobbintydepth.t y Twotydiffere
nttylevelsty(lowtyandtyhigh)tyoftyeachtyfactortyweretychosen,tyandtyatysingletyobservationtyontyflowtywastymadetyfortyea
chtycombinationtyoftylevels.
a. Thetyresultingtydatatysettyconsistedtyoftyhowtymanytyobservations?
b. Istythistyantyenumerativetyortyanalytictystudy?tyExplaintyyourtyreasoning.
ANS:
a. Numbertyobservationstyequalty2tyty 2tyt y 2=8
b. Thistycouldtybetycalledtyantyanalytictystudytybecausetythetydatatywouldtybetycollectedtyontyantyexistin
gtyprocess.tyTheretyistynotysamplingtyframe.
PTS:t y t y 1
5. Thetyaccompanyingtydatatyspecifictygravitytyvaluestyfortyvarioustywoodtytypestyusedtyintyconstructionty.
.41 .41 .42 .42. .42 .42 .42 .43 .44
.54 .55 .58 .62 .66 .66 .67 .68 .75
.31 .35 .36 .36 .37 .38 .40 .40 .40
.45 .46 .46 .47 .48 .48 .48 .51 .54
Constructtyatystem-and-leaftydisplaytyusingtyrepeatedtystemstyandtycommenttyontyanytyinterestingtyfeaturestyoftythetydisplay.
ANS:
OnetymethodtyoftydenotingtythetypairstyoftystemstyhavingtyequaltyvaluestyistytotydenotetythetystemtybytyL,tyforty‗low‘tya
ndtythetysecondtystemtybytyH,tyforty‗high‘.t y Usingtythistynotation,tythetystem-and-
leaftydisplaytywouldtyappeartyastyfollows:
3L 1 stem:tytenths
3H 56678 leaf:t y hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
Thetystem-and-
leaftydisplaytyontythetyprevioustypagetyshowstythatty.45tyistyatygoodtyrepresentativetyvaluetyfortythetydata.t y Intyadditio
n,tythetydisplaytyistynottysymmetrictyandtyappearstytotybetypositivelytyskewed.t y Thetyspreadtyoftythetydatatyisty.75ty-
ty.31ty=ty.44,tywhichtyisty.44/.45ty=ty.978tyortyaboutty98%tyoftythetytypicaltyvaluetyofty.45.t y Thistyconstitutestyatyreaso
nablytylargetyamounttyoftyvariationtyintythetydata.t y Thetydatatyvaluety.75tyistyatypossibletyoutlier.
PTS:t y t y 1
6. Temperaturetytransducerstyoftyatycertaintytypetyaretyshippedtyintybatchestyofty50.t y Atysampletyofty60tybatchestywasty
selected,tyandtythetynumbertyoftytransducerstyintyeachtybatchtynottyconformingtytotydesigntyspecificationstywastydet
ermined,tyresultingtyintythetyfollowingtydata:
0 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
4t y t y 2t y t y
1t y t y 3
2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
1t y t y 2t y t y
4t y t y 0
,5 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
0t y t y 2t y t y
3t y t y 2
, a. Determinetyfrequenciestyandtyrelativetyfrequenciestyfortythetyobservedtyvaluestyoftyxty=tynumbertyof
nonconformingtytransducerstyintyatybatch.
b. Whattyproportiontyoftybatchestyintythetysampletyhastyattymosttyfourtynonconformingtytransducers?tyWhattyprop
ortiontyhastyfewertythantyfour?tyWhattyproportiontyhastyattyleasttyfourtynonconformingtyunits?
ANS:
a.
NumbertyNonconforming Frequency RelativetyFrequency
0 7 0.117
1 12 0.200
2 13 0.217
3 14 0.233
4 6 0.100
5 3 0.050
6 3 0.050
7 1 0.017
8 1 0.017
1.001
Thetyrelativet y frequenciestydon’ttyaddtyuptyexactlytytoty1becausetytheytyhavetybeentyrounded
b.tyThetynumbertyoftybatchestywithtyattymostty4tynonconformingtyitemstyisty7+12+13+14+6=52,tywhichtyistyatyproporti
ontyofty52/60=.867.tyThetyproportiontyoftybatchestywithty(strictly)tyfewertythanty4tynonconformingtyitemstyisty46/60
=.767.
PTS:t y t y 1
7. Thetynumbertyoftycontaminatingtyparticlestyontyatysilicontywafertypriortytotyatycertaintyrinsingtyprocesstywastydetermin
edtyfortyeachtywafertyintyatysampletysizety100,tyresultingtyintythetyfollowingtyfrequencies:
Numbertyoft y particles Frequency Numbertyoft y particles Frequency
0 1 8 12
1 2 9 4
2 3 10 5
3 12 11 3
4 11 12 1
5 15 13 2
6 18 14 1
7 10
a. Whattyproportiontyoftythetysampledtywaferstyhadtyattyleasttytwotyparticles?tyAttyleasttysixtyparticles?
b. Whattyproportiontyoftythetysampledtywaferstyhadtybetweentyfourtyandtyninetyparticles,tyinclusive?tyStrictlytybetwee
ntyfourtyandtyninetyparticles?
ANS:
a. Fromtythistyfrequencytydistribution,tythetyproportiontyoftywaferstythattycontainedtyattyleasttytwotyparticlestyisty(100-1-
2)/100ty=
.97,tyorty97%.tyIntyatysimilartyfashion,tythetyproportiontycontainingtyattyleastty6typarticlestyisty(100ty–ty1-2-3-12-
11-15)/100ty=ty56/100ty=ty.56,tyorty56%.
b. Thetyproportiontycontainingtybetweenty4tyandty9typarticlestyinclusivetyisty(11+15+18+10+12+4)/100ty=ty70/100t
y=ty.70,tyorty70%.tyThetyproportiontythattycontaintystrictlytybetweenty4tyandty9ty(meaningtystrictlytymoretythanty4ty
andtystrictlytylesstythanty9)tyisty(15+ty18+10+12)/100=ty55/100ty=ty.55,tyorty55%.
