M. Khoshnevisan, R. Singh, P. Chauhan, N. Sawan and F. Smarandache (A general family of estimators for estimating population mean wing known value of some population parameter(s), Far East Journal of Theoretical Statistics 22, 181-191, 2007) introduced a family of estimators using auxiliary information in simple random sampling. They showed that these estimators are more efficient than the classical ratio estimator and that the minimum value of the mean square error (MSE) of this family is equal to the MSE of the regression estimator. In this paper we propose another family of estimators using the results of B. Prasad (Some improved ratio type estimators of population mean and ratio in finite population sample surveys, Communications in Statistics: Theory and Methods 18, 379-392, 1989). Expressions for the bias and MSE of the proposed family are derived. Besides, considering the minimum cases of these MSE equations, a comparison of the efficiency conditions between the Khoshnevisan and proposed families are obtained. The proposed family of estimators is found to be more efficient than Khoshnevisan's family of estimators under certain conditions. Finally, these theoretical findings are illustrated by a numerical example with original data.