we have $Y=\frac{(\bar{R}-\mu)}{\sigma / \sqrt{N}} \sim N(0,1)$ and $\frac{v \mathrm{-s}^{2}}{\sigma^{2}} \sim \chi^{2} (v)$ - Can easily shows that $\frac{(\bar{R}-\mu)}{s / \sqrt{N}} \sim \mathbf{t}(v) \quad$ Prove it $$ SP.PC.132