please may you resolve the proplem a full answer thanks

Apr 9th, 2015
RockCafe
Category:
Statistics
Price: $15 USD

Question description

Inthe1980s,random drug-testingpoliciesdesignedtoidentify individuals whowereusingillegaldrugs  becamepopular within governmentand civilianorganiza- tions. Hereisasummary ofthefactscitedbytheleaderofafictitious “XYZorganiza- tion” tosupportsuchpolicies:

• Druguseisaseriousproblem for(XYZorganization)and  wecannot tolerate drug userswithin ourranks.  Consequently,Iwanteachdivisionleader  tosendat least  five individuals perweekforrandom drug testing.  The test is99%accurate inidentifying drugusers. Nowwecanfindthedrugusersandseparate them fromtheorganization.

•99%ofourpeopledon’tusedrugs.

•There’snoplacein(XYZorganization)forthe1%whoaredrugusers. UsingBayes’Rule,evaluate theefficacyofsuchadrugtesting policy:

a)Assumeprior probabilitiesof1%fordrug usersand 99%fornon-drug userswithin the populationofXYZ.(The seniorleader said,1%ofthe XYZpopulationconsistsof drugusers).

b)A“positive” drugtestindicates thatanindividual islikelyadruguser. A“negative”

result indicates thattheindividual islikelynotadruguser.

c)Assumethatanindividual whoactually usesillegaldrugs willtest positive 99%of the time, and anon-drug usertests positive 1%ofthe time whenarandom drug test isadministered. Conversely, anon-drug userwilltest negative 99%ofthe time, and a

druguserwilltest negative 1%ofthetime.

d)Estimatethe probabilitythatanindividual isinfactadrug userifadrug test ad- ministered totheindividual results ina“positive.”

word the last Q.docx

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