A Simulated Data Analysis on the Interval Estimation for the Binomial Proportion P

Abstract

This study constructed a quadratic-based interval estimator for binomial proportion p. The modified method imposed a continuity correction over the confidence interval. This modified quadratic-based interval was compared to the different existing alternative intervals through numerical analysis using the following criteria: coverage probability, and expected width for various values of n, p and ? = 0.05. Simulated data results generated the following observations: (1) the coverage probability of modified interval is larger compared to that of the standard and non-modified intervals, for any p and n; (2) the coverage probability of all the alternative methods approaches to the nominal 95% confidence level as n increases for any p;(3) the modified and non-modified intervals have indistinguishable width differences for any p as n gets larger; (4) the expected width of the modified and alternative intervals decreases as n increases for  and any p. Based on these observations one can say that the modified method is an improvement of the standard method. It is therefore recommended to modify other existing alternative methods in such a way that there’s an increase in performance in terms of coverage properties, expected width, and other measures.

Keywords: Confidence Interval, Binomial Distribution, Standard Interval, Coverage Probability, Expected Width