J.I. Mbegbu

This study evaluated and compared the performance of three statistical methods for hypothesis testing when comparing means between two populations: the t-test, Welch's t-test, and the z-test. The t-test assumes normally distributed data and equal variances, while Welch's t-test accounts for unequal variances, and the nonparametric Mann- Whitney U test is an alternative for non-normal data. The research aimed to determine the optimal test by formulating hypotheses, selecting appropriate test statistics, determining sample sizes, and implementing the tests using R programming. The data analyzed were the mean heights of NBA guards and forwards during the 2022-2023 season. A power analysis assessed the reliability, validity, and assumptions of the tests. The results indicated a significant difference in mean heights between guards and forwards, with guards being slightly taller on average. Importantly, the Welch's t-test consistently outperformed the standard t-test and z-test across varying sample sizes, demonstrating higher power and a greater ability to detect true effects while minimizing Type I and Type II errors. This superior performance is attributed to the robustness of Welch's t-test in handling unequal variances between groups, a common scenario in real -world data analysis.