Table 1. The relative root mean square error of the new ratio estimators and associated variance estimators for N = 3,000.

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 known		$\overline{X}$ is unknown		$\overline{X}$ 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	100	0.0470	0.0472	0.0465	0.0467	0.1702	0.1703	0.2763	0.3201
	200	0.0350	0.0351	0.0354	0.0361	0.1321	0.1316	0.1761	0.2069
	600	0.0322	0.0324	0.0330	0.0340	0.1150	0.1158	0.1408	0.1658
	1,200	0.0104	0.0105	0.0105	0.0107	0.0427	0.0697	0.0512	0.0804
80	100	0.0364	0.0373	0.0366	0.0375	0.1453	0.1490	0.1930	0.2526
	200	0.0258	0.0261	0.0266	0.0269	0.1127	0.1141	0.1855	0.2048
	600	0.0134	0.0139	0.0146	0.0150	0.0588	0.0614	0.1108	0.1149
	1,200	0.0086	0.0089	0.0088	0.0090	0.0433	0.0552	0.0660	0.0875