Table 4.

Behavior of the Wald confidence interval width ${\stackrel{\sim }{W}}_{\mathrm{W}}$ as compared to the fixed value ${\pi }_0=\frac{1}{2}$ and α = 0.05.

Sample size	w0	$P\left({\stackrel{\sim }{W}}_{\mathrm{W}}<w_0|{\pi }_0=\frac{1}{2}\right)$	$E\left({\stackrel{\sim }{W}}_{\mathrm{W}}|{\pi }_0=\frac{1}{2}\right)$	n*	CPn	${\text{CP}}_{n^{\ast }}$
10	0.6198	0.7539	0.5856	8	0.8907	0.9307
11	0.5910	1.0000	0.5617	9	0.9342	0.8198
100	0.1960	0.9204	0.1950	98	0.9439	0.9466
101	0.1950	1.0000	0.1941	99	0.9545	0.9567
200	0.1386	0.9437	0.1382	198	0.9454	0.9456
201	0.1382	1.0000	0.1379	199	0.9518	0.9538
1000	0.0620	0.9748	0.0619	998	0.9458	0.9457
1001	0.0619	1.0000	0.0619	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 $E\left({\stackrel{\sim }{W}}_{\mathrm{W}}|{\pi }_0=\frac{1}{2}\right)>w_0$; CP_n, coverage probability for sample size n; ${\text{CP}}_{n^{\ast }}$, coverage probability for sample size n*.