Determining Sample Size for the Means of the Exponential Distribution: Considering Hypothesis Testing, Confidence Intervals, Prediction Intervals, and Cost Constraints

This study presents a unified framework for determining sample sizes in exponential distributions, addressing both hypothesis testing and the construction of confidence intervals. The method prevents underestimation, ensuring adequate power and precision. It extends to optimal allocation in two-sample problems under cost constraints and to sample size planning for prediction intervals in replication studies. To support practice, four user-friendly R Shiny apps were developed. Monte Carlo simulations confirm accuracy, with reliable coverage and error control. Applications under Type I and Type II censoring are illustrated with a leukemia treatment example. Overall, the framework offers practical tools for determining rigorous sample sizes in exponential modeling.