Inestimatingtheprobability of the yes responseonasensitivequestion,themethodof randomizedresponse can beusedtoencouragesubjectstomakeresponses.Thesubjectis askedtoflipacoin,insecret.Ifitisahead,thesubjecttossesthecoinoncemoreandreports the outcome,headortails.If,instead,thefirstflipisatail,thesubjectreportsinsteadthe responsetothesensitivequestion,reporting head if thetrueresponseis yes

Inestimatingtheprobability π of the yes responseonasensitivequestion,themethodof randomizedresponse can beusedtoencouragesubjectstomakeresponses.Thesubjectis askedtoflipacoin,insecret.Ifitisahead,thesubjecttossesthecoinoncemoreandreports the outcome,headortails.If,instead,thefirstflipisatail,thesubjectreportsinsteadthe responsetothesensitivequestion,reporting head if thetrueresponseis yes and reporting tail if thetrueresponseis no.

(a) Explainwhythevaluesin Table4.5 are theprobabilitiesofthefourpossibleoutcomes.

(b) Let ˜π denote thesampleproportionofsubjectswhoreport head for thesecondresponse.

Explain why 2˜π −