Table 6.

Behavior of the Wald confidence interval width ${\stackrel{\sim }{W}}_{\mathrm{W}}$ as compared to the fixed value w₀ at π₀ = 0.975 and α = 0.05.

Sample size	w0	$P\left({\stackrel{\sim }{W}}_{\mathrm{W}}<w_0|{\pi }_0=0.975\right)$	$E\left({\stackrel{\sim }{W}}_{\mathrm{W}}|{\pi }_0=0.975\right)$	n*	CPn	${\text{CP}}_{n^{\ast }}$
10	0.1935	0.7763	0.0864	NAb	0.2256	NAb
11	0.1845	0.7569	0.0862	NAb	0.2428	NAb
100	0.0612	0.5422	0.0565	80	0.9163	0.8635
101	0.0609	0.5357	0.0563	81	0.9180	0.8664
200	0.0433	0.4383	0.0420	187	0.8724	0.9410
201	0.0432	0.6115	0.0419	188	0.8740	0.9477
1000	0.0194	0.4724	0.0193	989	0.9497	0.9481
1001	0.0193	0.5509	0.0192	990	0.9287	0.9488
2000	0.0137	0.4805	0.0136	1989	0.9397	0.9500
2001	0.0137	0.5361	0.0136	1990	0.9393	0.9508

Notes: n*, suggested sample size based on $E\left({\stackrel{\sim }{W}}_{\mathrm{W}}|{\pi }_0=0.975\right)>w_0$; CP_n, coverage probability for sample size n; ${\text{CP}}_{n^{\ast }}$, coverage probability for sample size n*;

^b, n* and ${\text{CP}}_{n^{\ast }}$ are not attainable for the corresponding sample size.