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1、CHAPTER1SOLUTIONSTOPROBLEMS1.1(i)Ideally,wecouldrandomlyassignstudentstoclassesofdifferentsizes.Thatis,eachstudentisassignedadifferentclasssizewithoutregardtoanystudentcharacteristicssuchasabilityandfamilybackground.ForreasonswewillseeinChapter2,wewouldlikesu
2、bstantialvariationinclasssizes(subject,ofcourse,toethicalconsiderationsandresourceconstraints).(ii)Anegativecorrelationmeansthatlargerclasssizeisassociatedwithlowerperformance.Wemightfindanegativecorrelationbecauselargerclasssizeactuallyhurtsperformance.Howev
3、er,withobservationaldata,thereareotherreasonswemightfindanegativerelationship.Forexample,childrenfrommoreaffluentfamiliesmightbemorelikelytoattendschoolswithsmallerclasssizes,andaffluentchildrengenerallyscorebetteronstandardizedtests.Anotherpossibilityisthat,
4、withinaschool,aprincipalmightassignthebetterstudentstosmallerclasses.Or,someparentsmightinsisttheirchildrenareinthesmallerclasses,andthesesameparentstendtobemoreinvolvedintheirchildren’seducation.(iii)Giventhepotentialforconfoundingfactors–someofwhichareliste
5、din(ii)–findinganegativecorrelationwouldnotbestrongevidencethatsmallerclasssizesactuallyleadtobetterperformance.Somewayofcontrollingfortheconfoundingfactorsisneeded,andthisisthesubjectofmultipleregressionanalysis.1.2(i)Hereisonewaytoposethequestion:Iftwofirms
6、,sayAandB,areidenticalinallrespectsexceptthatfirmAsuppliesjobtrainingonehourperworkermorethanfirmB,byhowmuchwouldfirmA’soutputdifferfromfirmB’s?(ii)Firmsarelikelytochoosejobtrainingdependingonthecharacteristicsofworkers.Someobservedcharacteristicsareyearsofsc
7、hooling,yearsintheworkforce,andexperienceinaparticularjob.Firmsmightevendiscriminatebasedonage,gender,orrace.Perhapsfirmschoosetooffertrainingtomoreorlessableworkers,where“ability”mightbedifficulttoquantifybutwhereamanagerhassomeideaabouttherelativeabilitieso
8、fdifferentemployees.Moreover,differentkindsofworkersmightbeattractedtofirmsthatoffermorejobtrainingonaverage,andthismightnotbeevidenttoemployers.(iii)Theamountofcapitalandtechnologyavaila
