Table 2.

Behavior of the Agresti–Coull confidence interval width ${\stackrel{\sim }{W}}_{\text{AC}}$ as compared to the fixed value w₀ at π₀ = 0.95 and α = 0.05.

Sample size	w0	$P({\stackrel{\sim }{W}}_{\mathrm{AC}}<w_0|{\pi }_0=0.95)$	$E({\stackrel{\sim }{W}}_{\mathrm{AC}}|{\pi }_0=0.95)$	n*	CPn	${\text{CP}}_{n^{\ast }}$
10	0.4002	0.5987	0.3948	9	0.9882	0.9289
11	0.3790	0.5688	0.3737	10	0.9842	0.9886
100	0.0959	0.4360	0.0945	97	0.9663	0.9699
101	0.0954	0.6070	0.0940	98	0.9641	0.9691
200	0.0644	0.4547	0.0638	196	0.9659	0.9516
201	0.0642	0.5766	0.0636	197	0.9662	0.9703
1000	0.0274	0.4797	0.0273	995	0.9522	0.9519
1001	0.0274	0.5346	0.0273	996	0.9510	0.9518
2000	0.0192	0.4857	0.0192	1994	0.9537	0.9490
2001	0.0192	0.5245	0.0192	1995	0.9537	0.9488

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