Table 8.

Behavior of the Wilson (Score) confidence interval width ${\stackrel{\sim }{W}}_{\mathrm{S}}$ as compared to the fixed value w₀ at π₀ = 0.95 and α = 0.05.

Sample size	w0	$P\left({\stackrel{\sim }{W}}_{\mathrm{S}}<w_0|{\pi }_0=0.95\right)$	$E\left({\stackrel{\sim }{W}}_{\mathrm{S}}|{\pi }_0=0.95\right)$	n*	CPn	${\text{CP}}_{n^{\ast }}$
10	0.3393	0.5987	0.3274	9	0.9136	0.9289
11	0.3216	0.5688	0.3102	10	0.8968	0.9138
100	0.0902	0.4360	0.0884	96	0.9663	0.9422
101	0.0897	0.6070	0.0879	97	0.9641	0.9706
200	0.0622	0.4547	0.0615	195	0.9659	0.9524
201	0.0620	0.5766	0.0613	196	0.9662	0.9529
1000	0.0272	0.4797	0.0271	994	0.9522	0.9521
1001	0.0272	0.5346	0.0271	995	0.9510	0.9518
2000	0.0192	0.4857	0.0191	1994	0.9537	0.9490
2001	0.0192	0.5245	0.0191	1995	0.9537	0.9488

Notes: n*, suggested sample size based on $E\left({\stackrel{\sim }{W}}_{\mathrm{S}}|{\pi }_0=0.95\right)>w_0$; CP_n, coverage probability for sample size n; ${\text{CP}}_{n^{\ast }}$, coverage probability for sample size n*.