Improvement in estimating the population mean in simple random sampling using information on auxiliary attribute A.M. Abd-Elfattah * , E.A. El-Sherpieny, S.M. Mohamed, O.F. Abdou Institute of Statistical Studies and Research, Cairo University, Dokki, Giza 12613, Egypt article info Keywords: Ratio-type estimator Simple random sampling Auxiliary attribute Efficiency abstract This paper proposes some estimators for the population mean by adapting the estimator in Singh et al. (2008) [5] to the ratio estimators presented in Kadilar and Cingi 2006 [2]. We obtain mean square error (MSE) equation for all proposed estimators, and show that all proposed estimators are always more efficient than ratio estimator in Naik and Gupta (1996) [3], and Singh et al. (2008) [5]. The results have been illustrated numerically by tak- ing some empirical population considered in the literature. Ó 2009 Elsevier Inc. All rights reserved. 1. Introduction Consider a sample of size n drawn by simple random sample without replacement from a population of size N. Let y i and u i denoted the observation on variable y and u, respectively, for ith unit ði ¼ 1; 2; 3; ... ; NÞ. Suppose there is a complete dichotomy in the population with respect to the presence or absence of an attribute, say u, and it is assumed that attribute u takes only the two values 0 and 1 according as u ¼ 1; if ith unit of the population possesses attribute u ¼ 0; if otherwise: Let A ¼ P N i¼1 u i and a ¼ P n i¼1 u i denoted the total number of units in the population and sample possessing attribute u, respectively. Let P ¼ A N and b P ¼ a n denoted the proportion of units in the population and sample, respectively, possessing attri- bute u. Taking into consideration the point biserial correlation coefficient between auxiliary attribute and study variable, Naik and Gupta [3] defined ratio estimator of population mean when the prior information of population proportion of units, possessing the same attribute is available, as follows: t NG ¼  y P b P ; ð1:1Þ where  y is the sample mean of study variable. The MSE of t NG up to the first order of approximation is MSEðt NG Þ¼ 1  f n   S 2 y þ R 2 1 S 2 u  2R 1 S yu h i ; ð1:2Þ where f ¼ n N ; n is the sample size; N is the number of units in the population; R 1 ¼ Y P ; S 2 u is the population variance of aux- iliary attribute u, and S yu is the population covariance between variable of interest and auxiliary attribute u. 0096-3003/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2009.12.041 * Corresponding author. Address: Department of Statistics, Faculty of Science, King Abdul Aziz University Box 80203, Jedda 21589, Saudia Arabia. E-mail address: a_afattah@hotmail.com (A.M. Abd-Elfattah). Applied Mathematics and Computation 215 (2010) 4198–4202 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc