设X_1,X_2,...,X_m和Y_1,Y_2,...,Y_n分别取自两个相互独立的正态总体N(mu_1,sigma_1^2)及N(mu_2,sigma_2^2),则服从F(m-1,n-1)的统计量是()

设$X_1,X_2,\cdots,X_m$和$Y_1,Y_2,\cdots,Y_n$分别取自两个相互独立的正态总体$N(\mu_1,\sigma_1^2)$及$N(\mu_2,\sigma_2^2)$,则服从$F(m-1,n-1)$的统计量是()

• A. $\mu_1$及$\mu_2$已知,$F=\frac{\sigma_1^2}{\sigma_2^2}$,其中$\sigma_1^2=\frac{1}{m}\sum_{i=1}^{m}(X_i-\mu_1)^2,\sigma_2^2=\frac{1}{n}\sum_{j=1}^{n}(Y_j-\mu_2)^2$
• B. $\mu_1$及$\mu_2$未知,$F=\frac{S_1^2\sigma_1^2}{S_2^2\sigma_1^2}$,其中$S_1^2=\frac{1}{m-1}\sum_{i=1}^{m}(X_i-\overline{X})^2,S_2^2=\frac{1}{n-1}\sum_{j=1}^{n}(Y_j-\overline{Y})^2$
• C. $\sigma_1^2$及$\sigma_2^2$已知,$U=\frac{X_i-\overline{Y}}{\sqrt{\left(\frac{\sigma_1^2}{m}\right)^2+\left(\frac{\sigma_2^2}{n}\right)^2}}$
• D. $\sigma_1^2$及$\sigma_2^2$未知,$T=\frac{X_i-\overline{X}}{S_w\sqrt{\frac{1}{m}+\frac{1}{n}}}$,其中$S_w=\sqrt{\frac{(m-1)S_1^2+(n-1)S_2^2}{m+n-2}}$