Abstract
In the present paper we propose an alternative estimator of population mean, corresponding to Horvitz and Thompson [12] estimator, for multi-characteristics by using probability proportional to size and without replacement sampling when the auxiliary variable and hence the selection probabilities are poorly correlated with the study variable and are also sensitive in nature. The estimator is based on scrambled responses using Randomized Response Technique (RRT).The mean square error (MSE) expressions are derived for the proposed estimator. The behavior of the proposed estimator has been examined under super population model. An empirical study has also been carried out to look into the performance of the proposed estimator in comparison to the estimators existing in literature.