In this paper, we review the performance of Wald’s, score, exact and Jeffrey’s Confidence Intervals (CIs) with the objective to evaluate each CI and compare them in terms of their average coverage probabilities and average expected lengths. The Wald’s and exact intervals are most erratic, not reaching the nominal value established, and even when the sample size n is large enough. The expected lengths and coverage probabilities in the exact interval are the largest. The score and Jeffrey’s intervals generated best results, approaching the established nominal value. These are of smallest width in their average expected lengths, even when the sample size is small  An analysis has been performed for the four confidence intervals, with a real database, in the presence and absence of a disease in Agave tequilana plant, giving that score and Jeffrey’s were the best models to obtain the closest coverage probability to the nominal established value.

confidence intervals, average coverage probability, average expected length.

Received: October 4, 2023; Accepted: November 9, 2023; Published: December 30, 2023

How to cite this article: David A. Sotres-Ramos, Martha E. Ramírez-Guzmán, Gustavo Mora-Aguilera and Ollin T. Rodríguez-Bravo, Comparison of confidence intervals for the Bernoulli parameter, Far East Journal of Mathematical Education 26(1) (2024), 1-13. http://dx.doi.org/10.17654/0973563124001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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