Table 4.

The Monte Carlo Type I Errors and Powers of the EL ratio test statistics (3) and (7) for testing H₀: μ_x = 2 Based on Data Following the Hybrid Design ( $X_i~{\chi }_2^2+a$, ${\epsilon }_i~N(0,{\sigma }_m^2)$, and EX_i = 2 + a. The pooling proportion α = 0.5; the expected significance level was 0.05).

Sample Size (N)	Pooling Group Size (p)	Parameters ${\sigma }_m^2$	ELR Test Statistic (3)				ELR Test Statistic (7)
			Type I Error	Power			Type I Error	Power
			a = 0	a = 0.1	a = 0.2	a = 0.5	a = 0	a = 0.1	a = 0.2	a = 0.5
N=100	p=2	0.4	0.0687	0.0862	0.2021	0.8567	0.0724	0.0989	0.2144	0.7446
		1.0	0.0654	0.0792	0.1579	0.6978	0.0690	0.0936	0.1696	0.6417
	p=5	0.4	0.0649	0.1123	0.3133	0.9808	0.0985	0.1583	0.3552	0.9084
		1.0	0.0670	0.0906	0.1901	0.8141	0.0862	0.1131	0.2338	0.8171
	p=10	0.4	0.0646	0.1454	0.4460	0.9990	0.1016	0.1724	0.4416	0.9269
		1.0	0.0623	0.0916	0.2253	0.8776	0.0933	0.1241	0.2693	0.8744
N=200	p=2	0.4	0.0587	0.1137	0.3381	0.9907	0.0555	0.1210	0.3294	0.8227
		1.0	0.0544	0.0940	0.2583	0.9427	0.0534	0.1044	0.2612	0.8147
	p=5	0.4	0.0559	0.1699	0.5557	0.9998	0.0857	0.1903	0.5215	0.8944
		1.0	0.0538	0.1134	0.3366	0.9860	0.0770	0.1468	0.3687	0.9436
	p=10	0.4	0.0572	0.2279	0.7539	1.0000	0.0801	0.2027	0.6158	0.8875
		1.0	0.0568	0.1233	0.3988	0.9935	0.0815	0.1629	0.4219	0.9527