Hypothesis Designs for Three-Hypothesis Test Problems

Table 3

Hypothesis designs and test schemes for ${\mu }_{ASN}={\mu }_1\text{,}$$\alpha =\beta =0.002$.

$N$	Under Asymptotic formulas				Under Gaussian quadrature formulas				${\epsilon }_k\hspace{0.17em}\hspace{0.17em}(\text{\%})$
	$k$	$n_0$	$a$	$\tan \hspace{0.17em}\psi$	$k$	$n_0$	$a$	$\tan \hspace{0.17em}\psi$
5	1.7893	3.6290	3.6340	0.8947	1.7105	3.2864	3.4644	0.8553	4.61
10	1.2179	7.8334	5.3391	0.6090	1.1900	7.1875	5.2255	0.5950	2.34
15	0.9800	12.0973	6.6350	0.4900	0.9667	11.1560	6.5639	0.4834	1.38
20	0.8419	16.3926	7.7236	0.4210	0.8352	15.1594	7.6882	0.4176	0.80
25	0.7490	20.7080	8.6809	0.3745	0.7460	19.1851	8.6770	0.3730	0.40
30	0.6812	25.0379	9.5454	0.3406	0.6803	23.2266	9.5698	0.3402	0.13