Table 3.

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

Sample size	w0	$P\left({\stackrel{\sim }{W}}_{\text{AC}}<w_0|{\pi }_0=0.975\right)$	$E\left({\stackrel{\sim }{W}}_{\text{AC}}|{\pi }_0=0.975\right)$	n*	CPn	${\text{CP}}_{n^{\ast }}$
10	0.3831	0.7763	0.3801	9	0.9750	0.9804
11	0.3613	0.7569	0.3582	10	0.9693	0.9750
100	0.0777	0.5422	0.0763	97	0.9608	0.9650
101	0.0771	0.5357	0.0758	98	0.9864	0.9634
200	0.0497	0.4383	0.0490	195	0.9626	0.9668
201	0.0496	0.6115	0.0489	196	0.9626	0.9664
1000	0.0200	0.4724	0.0199	991	0.9466	0.9588
1001	0.0200	0.5509	0.0199	992	0.9474	0.9581
2000	0.0139	0.4805	0.0139	1990	0.9480	0.9564
2001	0.0139	0.5361	0.0139	1991	0.9469	0.9563

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