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1、CHAPTER1SOLUTIONSTOPROBLEMS1.1(i)Ideally,wecouldrandomlyassignstudentstoclassesofdifferentsizes.Thatis,eachstudentisassignedadifferentclasssizewithoutregardtoanystudentcharacteristicssuchasabilityandfamilybackground.ForreasonswewillseeinChapter2,wewouldlikesub
2、stantialvariationinclasssizes(subject,ofcourse,toethicalconsiderationsandresourceconstraints).(ii)Anegativecorrelationmeansthatlargerclasssizeisassociatedwithlowerperformance.Wemightfindanegativecorrelationbecauselargerclasssizeactuallyhurtsperformance.However
3、,withobservationaldata,thereareotherreasonswemightfindanegativerelationship.Forexample,childrenfrommoreaffluentfamiliesmightbemorelikelytoattendschoolswithsmallerclasssizes,andaffluentchildrengenerallyscorebetteronstandardizedtests.Anotherpossibilityisthat,wit
4、hinaschool,aprincipalmightassignthebetterstudentstosmallerclasses.Or,someparentsmightinsisttheirchildrenareinthesmallerclasses,andthesesameparentstendtobemoreinvolvedintheirchildren’seducation.(iii)Giventhepotentialforconfoundingfactors–someofwhicharelistedin(
5、ii)–findinganegativecorrelationwouldnotbestrongevidencethatsmallerclasssizesactuallyleadtobetterperformance.Somewayofcontrollingfortheconfoundingfactorsisneeded,andthisisthesubjectofmultipleregressionanalysis.1.2(i)Hereisonewaytoposethequestion:Iftwofirms,sayA
6、andB,areidenticalinallrespectsexceptthatfirmAsuppliesjobtrainingonehourperworkermorethanfirmB,byhowmuchwouldfirmA’soutputdifferfromfirmB’s?(ii)Firmsarelikelytochoosejobtrainingdependingonthecharacteristicsofworkers.Someobservedcharacteristicsareyearsofschoolin
7、g,yearsintheworkforce,andexperienceinaparticularjob.Firmsmightevendiscriminatebasedonage,gender,orrace.Perhapsfirmschoosetooffertrainingtomoreorlessableworkers,where“ability”mightbedifficulttoquantifybutwhereamanagerhassomeideaabouttherelativeabilitiesofdiffer
8、entemployees.Moreover,differentkindsofworkersmightbeattractedtofirmsthatoffermorejobtrainingonaverage,andthismightnotbeevidenttoemployers.(iii)Theamountofcapitalandtechnologyavaila
