This paper introduces a new two-stage randomized response model for estimating the mean of a sensitive quantitative random variable. The proposed model is obtained for both simple and stratified random sampling. The efficiency of the proposed estimator, under both sampling schemes, is investigated with respect to various estimators and it is found to be more efficient. Moreover, a new measure for evaluating the performance of any randomized response estimator is introduced. The measure considers the relative efficiency of the randomized response estimator, and the privacy protection it offers. The performance of the proposed estimator is examined using the new measure and it is found to have an overall better performance than its rival estimators. A real data example is also examined using the proposed model and various models from literature.