## two sided mann whitney u

two samples: $X_1,,,,,,,,,,,,,,,,X_15$ and $Y_1,,,,,,,Y_15$ and i need to find two sided hypothesis . Assuming normally dist, furthermore, I know how to get $\frac{n(n+m+1)}{2}$i.e e(variable) and $\frac{n*m(+1)}{12}$ ie var
So I got, pivotal qty $\frac{\over{X}-\mu}{\frac{\sigma}{\sqrt{n}}}$ and C.I $E(S_n)\frac{\pm z_0.025*var(S_n)}{\sqrt{n+m}$ If any one could see my logic of thinking and help me from here please