Confidence Intervals for the Population Proportion

KOH YEW MENG AND POOI AH HIN

Research Report No. 17/2001

Abstract

When the sample size is small, an approximate confidence interval for the population $p$ 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 form the desired value $1-\alpha$, and the average expected length is minimised. The performance of the resulting interval and that of the classical confidence intervals are compared.