Table 9.

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

Sample size	w0	$P\left({\stackrel{\sim }{W}}_{\mathrm{S}}<w_0|{\pi }_0=0.975\right)$	$E\left({\stackrel{\sim }{W}}_{\mathrm{S}}|{\pi }_0=0.975\right)$	n*	CPn	${\text{CP}}_{n^{\ast }}$
10	0.3108	0.7763	0.3036	9	0.9750	0.9804
11	0.2927	0.7569	0.2857	10	0.9693	0.975
100	0.0696	0.5422	0.0676	95	0.9608	0.9682
101	0.0692	0.5357	0.0672	96	0.9581	0.9664
200	0.0465	0.4383	0.0456	193	0.9626	0.9682
201	0.0463	0.6115	0.0454	194	0.9626	0.9677
1000	0.0197	0.4724	0.0196	990	0.9466	0.9485
1001	0.0196	0.5509	0.0196	991	0.9474	0.9477
2000	0.0138	0.4805	0.0138	1990	0.9480	0.9488
2001	0.0138	0.5361	0.0138	1991	0.9469	0.9488

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