A NEW EXPONENTIAL RATIO-TYPE ESTIMATOR FOR POPULATION MEAN IN DOUBLE SAMPLING

Abstract

This research proposed a new exponential ratio-type estimator in double sampling for population mean and the Mean Square Error (MSE) of the proposed estimator was derived. Efficiency comparisons were carried out to study the performances of the proposed estimator over the existing estimators using the Mean Square Error (MSE), Coefficient of Variation and Percent Relative Efficiencies (PREs). The data used in the research was a secondary data obtained from the payment voucher (April 2017) of the Akure South Local Government, Ondo State, Nigeria. The data includes the grade level, gross payment and tax of one thousand and twenty three (1,023) workers. The data obtained were analyzed using Microsoft Excel and Scilab software. The conditions that make the proposed estimator more efficient than other estimators were found. An empirical study was carried out to show the performance of the proposed estimator. On the basis of the Coefficient of Variation, Mean Square Errors and the Percent Relative Efficiencies of the estimators in the study. The best estimator among the estimators compared with the proposed estimator has value of Mean Square Error across the three levels as 21242.781, 64419.404, 213601.62 respectively while the proposed estimator has value of Mean Square error across the three levels as 21217.329, 50036.416 and 126091.24 respectively which shows that the proposed exponential ratio-type estimator is more efficient than the existing estimators since the proposed estimator has the minimum Mean Square Error. The proposed estimator has sample mean of 6354.7431, 6160.536 and 6434.8642 for level 1, 2 and 3 respectively. Percent Relative Efficiencies of the proposed estimator is higher than the other estimators in all the levels considered with numerical value 175.1181, 216.1132 and 286.3171 respectively.