Table 2. The relative root mean square error of the new ratio estimators and associated variance estimators with population size N = 300.

Response rate (%)	n	The relative root mean square error of the proposed estimators				The relative root mean square error of the variance estimators
		$\overline{X}$ is known		$\overline{X}$ is unknown		$\overline{X}$ is known		$\overline{X}$ is unknown
		$PRMSE\left({\hat{Y}}_R^{\mathrm{\prime }(2)}\right)$		$PRMSE\left({\hat{Y}}_R^{\mathrm{\prime }(3)}\right)$		$PRMSE\left(\hat{V}\left({\hat{Y}}_R^{\mathrm{\prime }(2)}\right)\right)$		$PRMSE\left(\hat{V}\left({\hat{Y}}_R^{\mathrm{\prime }(3)}\right)\right)$
		MAR	MCAR	MAR	MCAR	MAR	MCAR	MAR	MCAR
60	10	0.1166	0.1196	0.1169	0.1198	0.6605	0.6902	2.2661	2.7669
	20	0.1038	0.1056	0.1049	0.1067	0.5423	0.5452	1.3307	1.3510
	60	0.0624	0.0626	0.0631	0.0634	0.2420	0.2489	0.3666	0.4646
	120	0.0478	0.0479	0.0483	0.0485	0.1548	0.1829	0.2500	0.2634
80	10	0.0949	0.0962	0.0957	0.0968	0.4347	0.4533	2.2106	2.5923
	20	0.0863	0.0869	0.0869	0.0871	0.3722	0.3736	1.3123	1.3319
	60	0.0480	0.0484	0.0481	0.0485	0.2084	0.2150	0.3628	0.4144
	120	0.0298	0.0301	0.0298	0.0303	0.1392	0.1514	0.2164	0.2325