The a priori determination of a proper sample size necessary to achieve some specified power is an important problem encountered frequently in practical studies. To establish the needed sample size for a two-sample t test, researchers may conduct the power analysis by specifying scientifically important values as the underlying population means while using a variance estimate obtained from related research or pilot study. In order to take account of the variability of sample variance, this article considers two approaches to sample size determinations. One provides the sample size required to guarantee with a given assurance probability that the actual power exceeds the planned power. The other gives the necessary sample size such that the expected power attains the designated power level. The suggested paradigm of adjusted sample variance combines the existing procedures into one unified framework. Numerical results are presented to illustrate the usefulness and advantages of the proposed approaches that accommodate the stochastic nature of the sample variance. More importantly, supplementary computer programs are developed to aid the usefulness and implementation of the suggested techniques. The exposition helps to clarify discrepancy in the previous demonstration and to extend the development of sample size methodology.