This study develops and evaluates four distinct methods for constructing confidence intervals (CIs) for the parameter of the Arz distribution—a model newly employed in the analysis of lifetime data. The examined CI methods include the likelihood-based CI, the Wald-type CI, the bootstrap-t CI, and the bias-corrected and accelerated (BCa) bootstrap CI. To assess the performance of these approaches, both simulation studies and real-world data applications were employed. Evaluation metrics focused on empirical coverage probability (ECP) and average width (AW) across various scenarios. For computational efficiency, a closed-form expression was derived for the Wald-type CI. Simulation results indicate that the likelihood-based and Wald-type intervals consistently achieved ECPs close to the nominal 0.95 level under most conditions. In contrast, the bootstrap-t and BCa bootstrap methods tended to exhibit reduced coverage, particularly in small-sample scenarios. However, as sample sizes increased, the performance of these bootstrap methods improved, with ECPs gradually converging to the nominal level. Performance was also found to vary with parameter values. For lower values, all methods exhibited satisfactory performance, while at higher values and small sample sizes, the bootstrap-t and BCa methods demonstrated notably reduced ECPs. The practical utility of these methods was further supported by empirical findings from real-world applications, which reinforced the simulation-based conclusions and underscored the reliability and applicability of the proposed CI procedures.