Confidence intervals for a binomial proportion are very useful in statistical practice, particularly Wald confidence interval is preferred by its simplicity. However, it is known that this confidence interval performs poorly in terms of coverage probability and expected mean length. To improve the Wald method, several authors have proposed the adjustments. This adjusted method has been studied in some investigations and the corresponding confidence intervals are known as adjusted Wald confidence intervals. In this work, via the analysis of some specific examples, we illustrate the use of the adjusted Wald confidence interval for the four values of c more recommended in the literature about the theme and we note that one of them stands out for its better performance in terms of its length.

confidence interval, binomial proportion, Wald, shrinkage estimator.