UCF QMB 3200 Final Exam
Doublingytheysizeyofytheysampleywilly-yANSWER-
reduceytheystandardyerroryofytheymean
Theysampleymeanyisytheypointyestimatoryofy-yANSWER-U
Aysimpleyrandomysampleyofysizeynyfromyanyinfiniteypopulationyofysiz
eyNyisytoybeyselected.yEachypossibleysampleyshouldyhavey-
yANSWER-theysameyprobabilityyofybeingyselected
Whichyofytheyfollowingystatementsyregardingytheysamplingydistribu
tionyofysampleymeansyisyincorrect?y-yANSWER-
Theystandardydeviationyofytheysamplingydistributionyisytheystandard
ydeviationyofytheypopulation.
Aysimpleyrandomysampleyofysizeynyfromyanyinfiniteypopulationyisyays
ampleyselectedysuchythaty-yANSWER-
eachyelementyisyselectedyindependentlyyandyisyselectedyfromytheys
ameypopulation
Theyfactythatytheysamplingydistributionyofysampleymeansycanybeyapp
roximatedybyyaynormalyprobabilityydistributionywheneverytheysampl
eysizeybecomesylargeyisybasedyonythey-yANSWER-
centralylimitytheorem.
Clusterysamplingyisy-yANSWER-ayprobabilityysamplingymethod.
Theycentralylimitytheoremystatesythaty-yANSWER-
ifytheysampleysizeynyisylarge,ythenytheysamplingydistributionyofytheys
ampleymeanycanybeyapproximatedybyyaynormalydistribution.
Theyvalueyofythe
isyusedytoyestimateytheyvalueyofytheypopulationyparametery-
yANSWER-sampleystatistic
Theysamplingydistributionyofyisythey-yANSWER-
probabilityydistributionyofyallypossibleyvaluesyofytheysampleyproporti
on.
,Whichyofytheyfollowingyisynotyaysymbolyforyayparameter?y-yANSWER-
S.
Theysampleystatisticycharacteristicysyisytheypointyestimatoryofy-
yANSWER-σ..
,Theydistributionyofyvaluesytakenybyyaystatisticyinyallypossibleysample
syofytheysameysizeyfromytheysameypopulationyisycalledyay-yANSWER-
samplingydistribution.
Whichyofytheyfollowingyisyaypointyestimator?y-yANSWER-S.
Asyayruleyofythumb,ytheysamplingydistributionyofytheysampleyproporti
onycanybeyapproximatedybyyaynormalyprobabilityydistributionywheny-
yANSWER-n(1y-yp)y≥y5yandynpy≥y5.
Aysampleyofy92yobservationsyisytakenyfromyanyinfiniteypopulation.yTh
eysamplingydistributionyofyisyapproximatelyy-yANSWER-
normalybecauseyofytheycentralylimitytheorem.
TheycentralylimitytheoremyisyimportantyinyStatisticsybecauseyityenab
lesyreasonablyyaccurateyprobabilitiesytoybeydeterminedyforyeventsyi
nvolvingytheysampleyaveragey-yANSWER-
whenytheysampleysizeyisylargeyregardlessyofytheydistributionyofytheyv
ariable.
Theydistributionyofyvaluesytakenybyyaystatisticyinyallypossibleysampl
esyofytheysameysizeyfromytheysameypopulationyisytheysamplingydist
ributionyofy-yANSWER-Theysample
Whichyofytheseybestydescribesyaysamplingydistributionyofyaysta
tistic?y-yANSWER-
Ityisytheydistributionyofyallyofytheystatisticsycalculatedyfromyallyp
ossibleysamplesyofytheysameysampleysize.
Theyprobabilityydistributionyofyallypossibleyvaluesyofytheysampleypro
portionyisythey-yANSWER-samplingydistributionyofyp.
Foryayfixedyconfidenceylevelyandypopulationystandardydeviation,yify
weywouldylikeytoycutyourymarginyofyerroryinyhalf,yweyshouldytakeyays
ampleysizeythatyisy-yANSWER-
fourytimesyasylargeyasytheyoriginalysampleysize.
Weycanyreduceytheymarginyofyerroryinyanyintervalyestimateyofypybyyd
oingyanyyofytheyfollowingyexcepty-yANSWER-
increasingytheyplanningyvalueyp*ytoy.5.
, Whenycomputingytheysampleysizeyneededytoyestimateyayproportiony
withinyaygivenymarginyofyerroryforyayspecificyconfidenceylevel,ywhaty
planningyvalueyofypyshouldybeyusedywhenynoyestimateyofypyisyavaila
ble?y-yANSWER-0.50
Aystatisticsyteacherystartedyclassyoneydayybyydrawingytheynamesyofy
10ystudentsyoutyofyayhatyandyaskedythemytoydoyasymanyypushupsya
sytheyycould.yThey10yrandomlyyselectedystudentsyaveragedy15ypus
hupsyperypersonywithyaystandardydeviationyofy9ypushups.ySupposeyt
heydistributionyofytheypopulationyofynumberyofypushupsythatycanybe
ydoneyisyapproximatelyynormal.yWhichyofytheyfollowingystatements y
isytrue?y-yANSWER-
Aytydistributionyshouldybeyusedybecauseyσyisyunknown.
Theyzyvalueyforyay99%yconfidenceyintervalyestimationyisy-yANSWER-
2.58
Inyanyintervalyestimationyforyayproportionyofyaypopulation,ytheycritica
lyvalueyofyzyaty99%yconfidenceyisy-yANSWER-2.576.
Inyintervalyestimation,yasytheysampleysizeybecomesylarger,ythey
intervalyestimatey-yANSWER-
becomesynarrower.Inygeneral,yhigheryconfidenceylevelsyprovid
eylargeryconfidenceyintervals.
Oneywayytoyhaveyhighyconfidenceyandyaysmallymarginyofyerro
ryisytoy-yANSWER-increaseytheysampleysize.
Fromyaypopulationythatyisynormallyydistributed,yaysampleyofy30yele
mentsyisyselectedyandytheystandardydeviationyofytheysampleyisycom
puted.yForytheyintervalyestimationyofyμ,ytheyproperydistributionytoyus
eyisythey-yANSWER-tydistributionywithy29ydegreesyofyfreedom.
Asytheynumberyofydegreesyofyfreedomyforyaytydistributionyincreases
,ytheydifferenceybetweenytheytydistributionyandytheystandardynorm
alydistributiony-yANSWER-becomesysmaller.
Theyvalueyaddedyandysubtractedyfromyaypointyestimateyinyorderyto
ydevelopyanyintervalyestimateyofytheypopulationyparameteryisykno
wnyasythey-yANSWER-marginyofyerror.
Doublingytheysizeyofytheysampleywilly-yANSWER-
reduceytheystandardyerroryofytheymean
Theysampleymeanyisytheypointyestimatoryofy-yANSWER-U
Aysimpleyrandomysampleyofysizeynyfromyanyinfiniteypopulationyofysiz
eyNyisytoybeyselected.yEachypossibleysampleyshouldyhavey-
yANSWER-theysameyprobabilityyofybeingyselected
Whichyofytheyfollowingystatementsyregardingytheysamplingydistribu
tionyofysampleymeansyisyincorrect?y-yANSWER-
Theystandardydeviationyofytheysamplingydistributionyisytheystandard
ydeviationyofytheypopulation.
Aysimpleyrandomysampleyofysizeynyfromyanyinfiniteypopulationyisyays
ampleyselectedysuchythaty-yANSWER-
eachyelementyisyselectedyindependentlyyandyisyselectedyfromytheys
ameypopulation
Theyfactythatytheysamplingydistributionyofysampleymeansycanybeyapp
roximatedybyyaynormalyprobabilityydistributionywheneverytheysampl
eysizeybecomesylargeyisybasedyonythey-yANSWER-
centralylimitytheorem.
Clusterysamplingyisy-yANSWER-ayprobabilityysamplingymethod.
Theycentralylimitytheoremystatesythaty-yANSWER-
ifytheysampleysizeynyisylarge,ythenytheysamplingydistributionyofytheys
ampleymeanycanybeyapproximatedybyyaynormalydistribution.
Theyvalueyofythe
isyusedytoyestimateytheyvalueyofytheypopulationyparametery-
yANSWER-sampleystatistic
Theysamplingydistributionyofyisythey-yANSWER-
probabilityydistributionyofyallypossibleyvaluesyofytheysampleyproporti
on.
,Whichyofytheyfollowingyisynotyaysymbolyforyayparameter?y-yANSWER-
S.
Theysampleystatisticycharacteristicysyisytheypointyestimatoryofy-
yANSWER-σ..
,Theydistributionyofyvaluesytakenybyyaystatisticyinyallypossibleysample
syofytheysameysizeyfromytheysameypopulationyisycalledyay-yANSWER-
samplingydistribution.
Whichyofytheyfollowingyisyaypointyestimator?y-yANSWER-S.
Asyayruleyofythumb,ytheysamplingydistributionyofytheysampleyproporti
onycanybeyapproximatedybyyaynormalyprobabilityydistributionywheny-
yANSWER-n(1y-yp)y≥y5yandynpy≥y5.
Aysampleyofy92yobservationsyisytakenyfromyanyinfiniteypopulation.yTh
eysamplingydistributionyofyisyapproximatelyy-yANSWER-
normalybecauseyofytheycentralylimitytheorem.
TheycentralylimitytheoremyisyimportantyinyStatisticsybecauseyityenab
lesyreasonablyyaccurateyprobabilitiesytoybeydeterminedyforyeventsyi
nvolvingytheysampleyaveragey-yANSWER-
whenytheysampleysizeyisylargeyregardlessyofytheydistributionyofytheyv
ariable.
Theydistributionyofyvaluesytakenybyyaystatisticyinyallypossibleysampl
esyofytheysameysizeyfromytheysameypopulationyisytheysamplingydist
ributionyofy-yANSWER-Theysample
Whichyofytheseybestydescribesyaysamplingydistributionyofyaysta
tistic?y-yANSWER-
Ityisytheydistributionyofyallyofytheystatisticsycalculatedyfromyallyp
ossibleysamplesyofytheysameysampleysize.
Theyprobabilityydistributionyofyallypossibleyvaluesyofytheysampleypro
portionyisythey-yANSWER-samplingydistributionyofyp.
Foryayfixedyconfidenceylevelyandypopulationystandardydeviation,yify
weywouldylikeytoycutyourymarginyofyerroryinyhalf,yweyshouldytakeyays
ampleysizeythatyisy-yANSWER-
fourytimesyasylargeyasytheyoriginalysampleysize.
Weycanyreduceytheymarginyofyerroryinyanyintervalyestimateyofypybyyd
oingyanyyofytheyfollowingyexcepty-yANSWER-
increasingytheyplanningyvalueyp*ytoy.5.
, Whenycomputingytheysampleysizeyneededytoyestimateyayproportiony
withinyaygivenymarginyofyerroryforyayspecificyconfidenceylevel,ywhaty
planningyvalueyofypyshouldybeyusedywhenynoyestimateyofypyisyavaila
ble?y-yANSWER-0.50
Aystatisticsyteacherystartedyclassyoneydayybyydrawingytheynamesyofy
10ystudentsyoutyofyayhatyandyaskedythemytoydoyasymanyypushupsya
sytheyycould.yThey10yrandomlyyselectedystudentsyaveragedy15ypus
hupsyperypersonywithyaystandardydeviationyofy9ypushups.ySupposeyt
heydistributionyofytheypopulationyofynumberyofypushupsythatycanybe
ydoneyisyapproximatelyynormal.yWhichyofytheyfollowingystatements y
isytrue?y-yANSWER-
Aytydistributionyshouldybeyusedybecauseyσyisyunknown.
Theyzyvalueyforyay99%yconfidenceyintervalyestimationyisy-yANSWER-
2.58
Inyanyintervalyestimationyforyayproportionyofyaypopulation,ytheycritica
lyvalueyofyzyaty99%yconfidenceyisy-yANSWER-2.576.
Inyintervalyestimation,yasytheysampleysizeybecomesylarger,ythey
intervalyestimatey-yANSWER-
becomesynarrower.Inygeneral,yhigheryconfidenceylevelsyprovid
eylargeryconfidenceyintervals.
Oneywayytoyhaveyhighyconfidenceyandyaysmallymarginyofyerro
ryisytoy-yANSWER-increaseytheysampleysize.
Fromyaypopulationythatyisynormallyydistributed,yaysampleyofy30yele
mentsyisyselectedyandytheystandardydeviationyofytheysampleyisycom
puted.yForytheyintervalyestimationyofyμ,ytheyproperydistributionytoyus
eyisythey-yANSWER-tydistributionywithy29ydegreesyofyfreedom.
Asytheynumberyofydegreesyofyfreedomyforyaytydistributionyincreases
,ytheydifferenceybetweenytheytydistributionyandytheystandardynorm
alydistributiony-yANSWER-becomesysmaller.
Theyvalueyaddedyandysubtractedyfromyaypointyestimateyinyorderyto
ydevelopyanyintervalyestimateyofytheypopulationyparameteryisykno
wnyasythey-yANSWER-marginyofyerror.
