Mediation analysis is an important statistical tool in many research fields, where the joint significance test is widely utilized for examining mediation effects. Nevertheless, the limitation of this mediation testing method stems from its conservative Type I error, which reduces its statistical power and imposes certain constraints on its utility. The proposed solution to address this gap is the adjusted joint significance test for one mediator, which introduces a novel data-adjusted approach for assessing mediation effects that showcases significant advancements. The method is specifically designed to be user-friendly, thereby eliminating the necessity for intricate procedures. We further extend the adjusted joint significance test for small-scale mediation hypotheses with family-wise error rate (FWER) control. Additionally, a novel adjusted Sobel-type confidence interval is proposed for the mediation effects, demonstrating significant advancements over conventional Sobel's method. The effectiveness of our mediation testing and confidence interval estimation is assessed through extensive simulations, and compared against a multitude of existing approaches. Finally, we present the application of the method to three substantive datasets with continuous, binary and time-to-event outcomes, respectively.