ISYE 6644 - SUMMER 2024 - FINAL EXAM
QUESTIONS AND ANSWERS 100% CORRECT
1. What gis ga gpossible ggoal gof gan gindifference-zone gnormal gmeans
gselection gtech- gnique?:
ANS>> gFind gthe gnormal gpopulation ghaving gthe glargest gmean, gespecially gif gthe glargest gmean gis
gkthe gsecond-largest.
2. TRUE gor gFALSE? gThe gBechhofer gprocedure gfor gselecting gthe gnormal
gpopulation gwith gthe glargest gmean gspecifies gthe gappropriate
gnumber gof gobservations gto gtake gfrom geach gcompeting gpopulation,
gand gsimply gselects gthe gcompetitor ghaving gthe glargest gsample
gmean.:
gANS>> gTrue
3. TRUE gor gFALSE? gSometimes ga gsingle-stage gprocedure glike
gBechhofer's gis gin- gefficient. gIn gfact, git's gpossible gto guse gcertain
gsequential gprocedures gthat gtake gobservations gone-at-a-time
g(instead gof gall gat gonce gin ga gsingle gstage) gto gmake ggood
gselection gdecisions gusing gfewer gobservations.: g
ANS>> g gTrue
4. For g which g scenarios(s) g below g might g it g be g appropriate g to g use g a
g Bernoulli g selec- gtion gprocedure?
a) Find g the g inventory g policy g having g the g largest g profit.
b) Find g the g drug g giving g the g best g chance g of g a g cure.
c)Find g the g maintenance g policy g having g the g lowest g failure
g probability.
d) Find g the g scheduling g rule g that g that g has g the g best g chance g of
g making g an g on-time gdelivery.:
g ANS>> g gAll gthree gof g(b), g(c), gand g(d).
5. Suppose g that g a g Bernoulli g selection g procedure g tells g you g to g take
1 g/
g29
,ISYE 6644 - SUMMER 2024 - FINAL EXAM
QUESTIONS AND ANSWERS 100% CORRECT
g 100 g obser- gvations g from g each g of g two g populations, g A g and g B. g It
g turns g out g that g A g gets g 85 gsuccesses gand gB ggets g46 gsuccesses. gWhat gdo
gyou gthink?: g
ANS>> g1) gA galmost gcertainly ghas ga ghigher gsuccess gprobability gthan gB.
2) gWe gcould've gprobably gstopped gsampling ga gbit gearlier g(i.e., gwith gfewer gthan g100 gobservations)
gbecause gA gwas gso gfar gahead gof gB.
6. For g which g scenarios(s) g below g might g it g be g appropriate g to g use
g a g multinomial g selection gprocedure?: g
ANS>> g gFind gthe gmost-popular gpolitical gcandidate.
7. Suppose gthat gwe gwant gto gknow gwhich gof gCoke, gPepsi gand
gDr.pepper gis gthe gmost gpopular. gWe gwould glike gto gmake gthe
gcorrect gselection gwith gprobability gof g at gleast gP*=0.90 gin gthe
gevent gthat gthe gration gof gthe ghighest-to-second-highest gpreference
gprobabilities ghappens gto gbe gat gleast g0*=1.4. gHow gmany gpeople
gdoes gthe gsingle-stage gprocedure gMbem grequire gus gto ginterview?: g
ANS>> g126
Go gto gthe gtable gin gthe gnotes gand gpick gott gthe gentry gfor gk=3, gP ^ =Æ0 . 9 0 , gand gθ ^ =Æ1 . 4 .
2 g/
g29
,ISYE 6644 - SUMMER 2024 - FINAL EXAM
QUESTIONS AND ANSWERS 100% CORRECT
8. Which gof gthe gfollowing gparameters gcan gyou gget gconfidence
gintervals gfor? gMeans
Variances
gQuantiles
Differences gbetween gthe gmeans gof gtwo gsystems: g
ANS>> gAll gof gthe gabove
9. If gwe ghave gan giid gnormal gsample gof gobservations, gX1, gX2,...Xn,
gwhat gprobabil- gity gdistribution gis gmost-commonly gused gto gobtain
gcofidence gintervals gfor gthe g mean?:
g ANS>> g gt
10. TRUE gor gFALSE? gThe gpaired gCI gfor gthe gdifferences gin gtwo
gmeans gis gdesigned gto gwork gespecially gwell gif gall gof gthe
gobservations gfrom gthe gfirst gpopulation gare g completely
gindependent gof gall gof gthe gobservations gfrom gthe gsecond
gpopulation.-
:g
ANS>> gFALSE. g{In gfact, git's geasier gto gdistinguish gbetween gthe gtwo gmeans gif gXi gis gpositively gcorrelated
gwith gYi. gThink gabout gmy gparallel gparking gexample gin gthe gclass gnotes.}
11. TRUE gor gFALSE? gYou gcan guse ga gversion gof gindependent
greplications gto gobtain gconfidence gintervals gfor gthe gdifference gin
gthe gmeans gfrom gtwo gsimulation gmod- gels.: g
ANS>> gTRUE
12. TRUE gor gFALSE? gThe gcommon grandom gnumbers gtechnique
gintentionally gin- gduces gpositive gcorrelation gbetween gtwo gsystems
g- gmuch glike ga gpaired-c5oa n fi - gdence ginterval.: g
ANS>> gTRUE
3 g/
g29
QUESTIONS AND ANSWERS 100% CORRECT
1. What gis ga gpossible ggoal gof gan gindifference-zone gnormal gmeans
gselection gtech- gnique?:
ANS>> gFind gthe gnormal gpopulation ghaving gthe glargest gmean, gespecially gif gthe glargest gmean gis
gkthe gsecond-largest.
2. TRUE gor gFALSE? gThe gBechhofer gprocedure gfor gselecting gthe gnormal
gpopulation gwith gthe glargest gmean gspecifies gthe gappropriate
gnumber gof gobservations gto gtake gfrom geach gcompeting gpopulation,
gand gsimply gselects gthe gcompetitor ghaving gthe glargest gsample
gmean.:
gANS>> gTrue
3. TRUE gor gFALSE? gSometimes ga gsingle-stage gprocedure glike
gBechhofer's gis gin- gefficient. gIn gfact, git's gpossible gto guse gcertain
gsequential gprocedures gthat gtake gobservations gone-at-a-time
g(instead gof gall gat gonce gin ga gsingle gstage) gto gmake ggood
gselection gdecisions gusing gfewer gobservations.: g
ANS>> g gTrue
4. For g which g scenarios(s) g below g might g it g be g appropriate g to g use g a
g Bernoulli g selec- gtion gprocedure?
a) Find g the g inventory g policy g having g the g largest g profit.
b) Find g the g drug g giving g the g best g chance g of g a g cure.
c)Find g the g maintenance g policy g having g the g lowest g failure
g probability.
d) Find g the g scheduling g rule g that g that g has g the g best g chance g of
g making g an g on-time gdelivery.:
g ANS>> g gAll gthree gof g(b), g(c), gand g(d).
5. Suppose g that g a g Bernoulli g selection g procedure g tells g you g to g take
1 g/
g29
,ISYE 6644 - SUMMER 2024 - FINAL EXAM
QUESTIONS AND ANSWERS 100% CORRECT
g 100 g obser- gvations g from g each g of g two g populations, g A g and g B. g It
g turns g out g that g A g gets g 85 gsuccesses gand gB ggets g46 gsuccesses. gWhat gdo
gyou gthink?: g
ANS>> g1) gA galmost gcertainly ghas ga ghigher gsuccess gprobability gthan gB.
2) gWe gcould've gprobably gstopped gsampling ga gbit gearlier g(i.e., gwith gfewer gthan g100 gobservations)
gbecause gA gwas gso gfar gahead gof gB.
6. For g which g scenarios(s) g below g might g it g be g appropriate g to g use
g a g multinomial g selection gprocedure?: g
ANS>> g gFind gthe gmost-popular gpolitical gcandidate.
7. Suppose gthat gwe gwant gto gknow gwhich gof gCoke, gPepsi gand
gDr.pepper gis gthe gmost gpopular. gWe gwould glike gto gmake gthe
gcorrect gselection gwith gprobability gof g at gleast gP*=0.90 gin gthe
gevent gthat gthe gration gof gthe ghighest-to-second-highest gpreference
gprobabilities ghappens gto gbe gat gleast g0*=1.4. gHow gmany gpeople
gdoes gthe gsingle-stage gprocedure gMbem grequire gus gto ginterview?: g
ANS>> g126
Go gto gthe gtable gin gthe gnotes gand gpick gott gthe gentry gfor gk=3, gP ^ =Æ0 . 9 0 , gand gθ ^ =Æ1 . 4 .
2 g/
g29
,ISYE 6644 - SUMMER 2024 - FINAL EXAM
QUESTIONS AND ANSWERS 100% CORRECT
8. Which gof gthe gfollowing gparameters gcan gyou gget gconfidence
gintervals gfor? gMeans
Variances
gQuantiles
Differences gbetween gthe gmeans gof gtwo gsystems: g
ANS>> gAll gof gthe gabove
9. If gwe ghave gan giid gnormal gsample gof gobservations, gX1, gX2,...Xn,
gwhat gprobabil- gity gdistribution gis gmost-commonly gused gto gobtain
gcofidence gintervals gfor gthe g mean?:
g ANS>> g gt
10. TRUE gor gFALSE? gThe gpaired gCI gfor gthe gdifferences gin gtwo
gmeans gis gdesigned gto gwork gespecially gwell gif gall gof gthe
gobservations gfrom gthe gfirst gpopulation gare g completely
gindependent gof gall gof gthe gobservations gfrom gthe gsecond
gpopulation.-
:g
ANS>> gFALSE. g{In gfact, git's geasier gto gdistinguish gbetween gthe gtwo gmeans gif gXi gis gpositively gcorrelated
gwith gYi. gThink gabout gmy gparallel gparking gexample gin gthe gclass gnotes.}
11. TRUE gor gFALSE? gYou gcan guse ga gversion gof gindependent
greplications gto gobtain gconfidence gintervals gfor gthe gdifference gin
gthe gmeans gfrom gtwo gsimulation gmod- gels.: g
ANS>> gTRUE
12. TRUE gor gFALSE? gThe gcommon grandom gnumbers gtechnique
gintentionally gin- gduces gpositive gcorrelation gbetween gtwo gsystems
g- gmuch glike ga gpaired-c5oa n fi - gdence ginterval.: g
ANS>> gTRUE
3 g/
g29
