A Stratified Randomized Response model is proposed to estimate the proportions of the persons with sensitive characteristic, such as addiction to drugs and other intoxicants, induced abortions, proneness to tax evasion, gambling habits, history of past involvement in crimes, … , etc. Estimates of the parameters of the suggested model are obtained by using Maximum Likelihood method. The optimal sample size and the optimal allocations of , for the stratified random sampling, are determined. The posterior probabilities are derived using estimates of the parameters of the suggested model, as prior probabilities. An application to the spread of addiction phenomenon between the students in the university level is given. Z-test is used to test the significance of difference between the proportions of the male and female students with addiction phenomenon. Chi-Square test is used to test whether there is any relation between the response and sex or educational level of the student