IJSRSET16221 | Received: 29 February 2016 | Accepted: 10 March 2016 | March-April 2016 [(2)2: 10-16 ] © 2016 IJSRSET | Volume 2 | Issue 2 | Print ISSN : 2395-1990 | Online ISSN : 2394-4099 Themed Section: Science and Technology 10 Modified Ratio Estimators for Population Mean Using Size of the Sample, Selected From Population Mohmmad Jerajuddin 1* , Jai Kishun 2 1 Consultant MIS (RCH-II), National Institute of Health and Family Welfare, New Delhi, India 2 Assistant Professor (Statistics & Demography), National Institute of Health and Family Welfare, New Delhi, India ABSTRACT This paper deals with a modified ratio estimator for the estimation of population mean of study variable using the size of the sample, selected from the population under SRSWOR. The bias and mean square error of the proposed estimator up to the first order of approximation is derived [Appendix]. The constants, biases and mean square errors (MSEs) are computed using the data from Murthy [1] and Mukhopadhyay [3]. The percent relative efficiencies (PREs) are also computed for both existed and proposed estimators and compare the results accordingly for justifying the betterment of the proposed estimators over other mentioned modified estimators. Keywords: Auxiliary Variable, Sample size, Simple Random Sampling, Bias, Mean Square Error, Relative Standard Error (RSE), Percent Relative Efficiency (PRE). Notations & Terminology Used in this paper: N – Population Size n – Sample Size n = N f Sampling Fraction X – Auxiliary Variable Y – Study Variable X,Y – Population Mean x,y – Sample Mean x y C ,C – Co-efficient of Variations of X and Y respectively x y S ,S – Population Standard Deviations of X and Y respectively xy S – Population Covariance between X and Y d M – Median of the auxiliary variable  – Correlation Co-efficient between X & Y 3 2 1 3 1 2 3 2 ( - ) ( -1)( - 2) N i i x N X X N N S        , Co-efficient of Skewness of the auxiliary variable 4 2 1 4 2 4 2 2 ( 1) ( - ) 3( 1) ( -1)( - 2)(N 3) ( 2)( 3) N i i x NN X X N N N S N N              , Co-efficient of Kurtosis of the auxiliary variable. j ˆ Y – Existed j th modified ratio estimator of Y p ˆ Y – Proposed modified ratio estimator of Y Bias( ) – Bias of the estimator MSE( ) – Mean square error of the estimator PRE( ) – Percent relative efficiency of the estimator I. INTRODUCTION Cochran (1940) had first made his contribution to introduce the ratio estimator in literature using known information of the auxiliary variable in improving the efficiency of the estimator of the population mean Y [4]. Assuming that the population mean of the auxiliary variable X is known, and correlation between study and auxiliary variable is positive (high) [2], [3]; an estimator R ˆ Y of population mean Y was introduced. The ratio estimator is given below. ˆ ˆ R y Y X RX x         , where y y ˆ R= x x  (1.1) Where y is the sample mean of the study variable Y, and it is assumed that the population mean X of auxiliary variable X is known. The ratio estimator defined in (1.1) is the classical ratio estimate [18].