Hypothesis Designs for Three-Hypothesis Test Problems

Table 4

Hypothesis designs and test schemes for ${\mu }_{ASN}={\mu }_1\text{,}$$\alpha =\beta =0.05$.

$N$	Under Asymptotic formulas				Under Gaussian quadrature formulas				${\varepsilon }_k\hspace{0.17em}\hspace{0.17em}(\text{\%})$
	$k$	$n_0$	$a$	$\tan \hspace{0.17em}\psi$	$k$	$n_0$	$a$	$\tan \hspace{0.17em}\psi$
5	1.3089	3.0237	2.5085	0.6545	1.1875	2.9124	2.4858	0.5938	10.22
10	0.8835	6.6369	3.7164	0.4418	0.8264	6.2545	3.8213	0.4132	6.91
15	0.7083	10.3268	4.6358	0.3542	0.6715	10.0000	4.8351	0.3358	5.48
20	0.6071	14.0566	5.4085	0.3036	0.5803	13.4993	5.6872	0.2902	4.62
25	0.5393	17.8118	6.0883	0.2697	0.5183	17.0061	6.4368	0.2592	4.05
30	0.4899	21.5853	6.7022	0.2450	0.4727	20.8842	7.1131	0.2364	3.64