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Suppose {Y 1 ,...,Y n } areIIDfromUniform(0, )Let T = / ,where =max( Y 1 ,...,Y n ). (a)Findthecumulativedistributionfunctionof T andshowthat T isapivotalquantity. (b)Constructa one-sided

Suppose{Y1,...,Yn}areIIDfromUniform(0,)LetT=/,where=max(Y1,...,Yn).

(a)FindthecumulativedistributionfunctionofTandshowthatTisapivotalquantity.

(b)Constructaone-sided(1)-CIoftheform(,U]forbasedonthepivotalquantityT.

(c)Usetheconfidenceintervalconstructedin(b)toproposearejectionrulefortesting

H0:=1againstHa:<1atlevel0.05.

(d)Supposeforthetestin(c),wenolongerspecifyaparticularlevelandwishtoreportap-valueinstead.Derivethe(unobservedrandom)p-valuepasafunctionof.

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