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1、Chapter10:HypothesisTesting10.1SeeDefinition10.1.10.2NotethatYisbinomialwithparametersn=20andp.a.Iftheexperimenterconcludesthatlessthan80%ofinsomniacsrespondtothedrugwhenactuallythedruginducessleepin80%ofinsomniacs,atypeIerrorhasoccurred.b.α=P(rejectH0
2、H0true)=P(Y≤12
3、p=.8)=.032(usingAppendixIII).c
4、.Iftheexperimenterdoesnotrejectthehypothesisthat80%ofinsomniacsrespondtothedrugwhenactuallythedruginducessleepinfewerthan80%ofinsomniacs,atypeIIerrorhasoccurred.d.β(.6)=P(failtorejectH0
5、Hatrue)=P(Y>12
6、p=.6)=1–P(Y≤12
7、p=.6)=.416.e.β(.4)=P(failtorejectH0
8、Hatrue)=P(Y>12
9、p=.4)=.021.10.3a.UsingtheBinomi
10、alTable,P(Y≤11
11、p=.8)=.011,soc=11.b.β(.6)=P(failtorejectH0
12、Hatrue)=P(Y>11
13、p=.6)=1–P(Y≤11
14、p=.6)=.596.c.β(.4)=P(failtorejectH0
15、Hatrue)=P(Y>11
16、p=.4)=.057.10.4Theparameterp=proportionofledgersheetswitherrors.a.Ifitisconcludedthattheproportionofledgersheetswitherrorsislargerthan.05,whenactuallythepropor
17、tionisequalto.05,atypeIerroroccurred.b.Bytheproposedscheme,H0willberejectedunderthefollowingscenarios(letE=error,N=noerror):Sheet1Sheet2Sheet3NN.NENENNEEN22Withp=.05,α=P(NN)+P(NEN)+P(ENN)+P(EEN)=(.95)+2(.05)(.95)+2(.05)(.95)=.995125.c.Ifitisconcludedthatp=.05,butinfactp>.05,atypeIIerroroccurred.23
18、d.β(pa)=P(failtorejectH0
19、Hatrue)=P(EEE,NEE,orENE
20、pa)=2p(1−p)+p.aaa10.5UnderH0,Y1andY2areuniformontheinterval(0,1).FromExample6.3,thedistributionofU=Y1+Y2is⎧u0≤u≤1g(u)=⎨⎩2−u1.95)=.05=α.22Test2:α=.05=P(U>c)=∫(2−u)du=2=2c+.5c.Solvingthequadraticgivesctheplausiblesolutionofc=1.684.200Ch
21、apter10:HypothesisTesting201Instructor’sSolutionsManual10.6TheteststatisticYisbinomialwithn=36.a.α=P(rejectH0
22、H0true)=P(
23、Y–18
24、≥4
25、p=.5)=P(Y≤14)+P(Y≥22)=.243.b.β=P(failtorejectH0
26、Hatrue)=P(
27、Y–18
28、≤3
29、p=.7)=P(15≤Y≤21
30、p=.7)=.09155.10.7a.False,H0isnotastatementinvolvingarandomquantity.b.False,forthesamer
31、easonasparta.c.True.d.True.e.False,thisisgivenbyα.f.i.True.ii.True.iii.False,βandαbehaveinverselytoeachother.10.8LetY1andY2havebinomialdistributionswithparametersn=15andp.a.α=P(rejectH0instage1
32、H0true)+P(rejectH0
