Coverage Performance of the Wald Interval for a Binomial Proportion Under Textbook Guidelines

One of the most fundamental statistical problems is the estimation of a binomial population proportion by means of a confidence interval. The most well-known method for obtaining such an interval is the Wald method. The focus of this thesis is to explore the coverage performance of the Wald method under the various guidelines for its use that have been given in standard statistical textbooks. Both conditions involving n and p as well as conditions involving n and p-hat are analyzed. We investigate coverage performance both unconditionally and conditionally for guidelines based on n and p-hat. Comparative results are provided in figures and tables for various sample sizes. After analyzing each condition with various sample sizes, we find where certain conditions outperform others. We find a few surprising results. We conclude by recommending a specific condition and provide a simple rule of thumb for when the Wald method performs well using this condition.