Confidence intervals for the population proportion (Q851518)

When the sample size is small, an approximate confidence interval for the population proportion \(p\) is obtained by finding all the values of \(p_0\) for which \(H_0:p=p_0\) is accepted. The acceptance region of the test is chosen such that the average discrepancy of the coverage probability of the resulting confidence interval from the desired value is \(1-\alpha\), and the average expected length is minimised. The performance of the resulting interval and that of the classical confidence intervals are compared.