The two-stage sequential test, suggested by Baker [2] for testing hypotheses $H_0:mu=mu_0$ and $H_1:mu=mu_1$ of $N(mu,sigma^2)$ with the unknown $sigma^2$ would not be amenable for applications unles some cluses on the choice of the first-stage sample size are available. The study in this paper is intended to shed some light on the size of the first-stage sample. An approximate method is used to estimate an optimal initial sample size that minimizes the average sample number. In brief, the optimal size is a strictly monotone decreasing function of the quantity $(mu_1-mu_0)/sigma$. Empirical and simulation results are used to ascertain the negligible effect of possible errors due to approximations and assumptions used.