Table 7.

Behavior of the Wilson (Score) confidence interval width ${\stackrel{\sim }{W}}_{\mathrm{S}}$ as compared to the fixed value w₀ at ${\pi }_0=\frac{1}{2}$ and α = 0.05.

Sample size	w0	$P\left({\stackrel{\sim }{W}}_{\mathrm{S}}<w_0|{\pi }_0=\frac{1}{2}\right)$	$E\left({\stackrel{\sim }{W}}_{\mathrm{S}}|{\pi }_0=\frac{1}{2}\right)$	n*	CPn	${\text{CP}}_{n^{\ast }}$
10	0.5268	0.7539	0.5066	8	0.9783	0.9307
11	0.5088	1.0000	0.4906	9	0.9342	0.9612
100	0.1923	0.9204	0.1914	98	0.9439	0.9466
101	0.1914	1.0000	0.1905	99	0.9545	0.9567
200	0.1373	0.9437	0.1369	198	0.9454	0.9456
201	0.1369	1.0000	0.1366	199	0.9518	0.9538
1000	0.0619	0.9748	0.0618	998	0.9458	0.9457
1001	0.0618	1.0000	0.0618	999	0.9510	0.9502
2000	0.0438	0.9822	0.0438	1998	0.9478	0.9487
2001	0.0438	1.0000	0.0438	1999	0.9510	0.9519

Notes: n*, suggested sample size based on $E\left({\stackrel{\sim }{W}}_{\mathrm{S}}|{\pi }_0=\frac{1}{2}\right)>w_0$; CP_n, coverage probability for sample size n; ${\text{CP}}_{n^{\ast }}$, coverage probability for sample size n*.