Table 2.

The empirical coverage probability and average length of 95% confidence interval of ${\pi }_0$ based on exact method, delta method, nonparametric bootstrap, and hybrid bootstrap; N = 3324.

					H Bootstrap
					$p_0=\hat{p}$
${\pi }_0$	$q_0$	Exact method CovP (Length)	Delta method CovP (Length)	Bootstrap CovP (Length)	CovP (Length)
1.2	97.0	0.969 (0.022)	0.956 (0.020)	0.953 (0.022)	0.969 (0.021)
1.2	98.0	0.971 (0.020)	0.956 (0.018)	0.955 (0.019)	0.954 (0.019)
1.2	98.4	0.967 (0.018)	0.952 (0.017)	0.952 (0.017)	0.953 (0.017)
1.2	98.6	0.965 (0.017)	0.950 (0.016)	0.948 (0.016)	0.952 (0.017)
1.2	98.8	0.964 (0.017)	0.954 (0.015)	0.952 (0.015)	0.956 (0.016)
1.2	99.0	0.959 (0.016)	0.947 (0.014)	0.945 (0.014)	0.953 (0.015)
1.2	99.2	0.960 (0.015)	0.950 (0.013)	0.948 (0.013)	0.946 (0.014)
1.2	99.4	0.962 (0.013)	0.952 (0.012)	0.951 (0.012)	0.938 (0.013)
1.2	99.6	0.963 (0.012)	0.953 (0.011)	0.951 (0.011)	0.943 (0.011)
1.2	99.8	0.965 (0.011)	0.957 (0.010)	0.955 (0.010)	0.939 (0.010)
1.2	99.9	0.955 (0.010)	0.948 (0.009)	0.952 (0.009)	0.945 (0.009)
1.2	100.0	0.943 (0.009)	0.943 (0.008)	0.945 (0.008)	0.923 (0.008)