t and F statistics from even and odd observations

Let $X_1,X_2,…,X_{50}$ be a random sample from a $N(0,\sigma^2)$ distribution, where $\sigma>0$. Define $$\bar X_e=\frac1{25}\sum_{i=1}^{25}X_{2i},\quad \bar X_o=\frac1{25}\sum_{i=1}^{25}X_{2i-1},$$ $$S_e=\sqrt{\frac1{24}\sum_{i=1}^{25}(X_{2i}-\bar X_e)^2}\quad\text{and}\quad S_o=\sqrt{\frac1{24}\sum_{i=1}^{25}(X_{2i-1}-\bar X_o)^2}.$$ Then which of the following statements is/are correct?