Hypothesis Designs for Three-Hypothesis Test Problems

Table 1

Hypothesis designs and test schemes for ${\mu }_{ASN}={\mu }_0\text{,}$$\alpha =\beta =0.002$.

$N$	Under Asymptotic formulas				Under Gaussian quadrature formulas				${\varepsilon }_k\hspace{0.17em}\hspace{0.17em}(\text{\%})$
	$k$	$n_0$	$a$	$\tan \psi$	$k$	$n_0$	$a$	$\tan \psi$
5	2.1090	2.6121	3.0831	1.0545	1.8953	2.6876	3.0725	0.9477	11.28
10	1.4400	5.6030	4.5155	0.7200	1.3193	5.8833	4.6576	0.6597	9.15
15	1.1604	8.6279	5.6034	0.5802	1.0674	9.0266	5.8910	0.5337	8.71
20	0.9977	11.6709	6.5170	0.4989	0.9228	12.3354	6.9039	0.4614	8.12
25	0.8882	14.7257	7.3204	0.4441	0.8246	15.6592	7.7944	0.4123	7.71
30	0.8082	17.7888	8.0458	0.4041	0.7523	18.9949	8.5984	0.3762	7.43