Minimization of Ratio Over-estimation Problem in Simple Random Sampling when Population Means are known

Abstract

In this study, the presence of over-estimation in the conventional ratio estimator ) ( r y on mean estimator ) (y when population means are known is being contested. Three categories of data sets were used to justify this work. Category A is when the population mean of auxiliary variable is lower than the population mean of the variable of interest ) ( Y X , category B is when the population mean of auxiliary variable is greater than the population mean of the variable of interest ) ( Y X while category C is when the population mean of auxiliary variable is the same as the population mean of the variable of interest ) ( Y X . It was observed that for all these categories evidences of over-estimation of r y onywere recorded whenever y x c c 2 . One of the earliest suggested alternatives, str y , also over estimated y when tested. Hence, an alternative, aaar y which utilizes the regression estimate of the study and auxiliary variables ) ( xy  under consideration was suggested and found to minimize over estimation of r y onywhenever 2 2 2 2 2 2 2 2 ) ( 2 ] ) ( ( )1 ) ( ( [ X X cc c X X X X c xy x y x xy xy y xy              , 7.0 1.0   .  The conclusion from this study is that aaar y may generally be used whenever problem of over estimation is encountered in ratio estimation.