Hypothesis Designs for Three-Hypothesis Test Problems

Table 2

Hypothesis designs and test schemes for ${\mu }_{ASN}={\mu }_0\text{,}$$\alpha =\beta =0.05$.

$N$	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	1.6066	2.0072	2.0438	0.8033	1.3025	2.1953	2.2175	0.6513	23.35
10	1.0908	4.3542	3.0102	0.5454	0.9087	5.0028	3.4233	0.4544	20.04
15	0.8767	6.7395	3.7450	0.4384	0.7401	8.0001	4.2242	0.3701	18.46
20	0.7527	9.1448	4.3624	0.3764	0.6392	11.0000	5.2525	0.3196	17.76
25	0.6693	11.5630	4.9054	0.3347	0.5708	14.0000	5.9086	0.2854	17.26
30	0.6085	13.9903	5.3957	0.3043	0.5204	17.0000	6.5244	0.2602	16.93