Test the Hypothesis That $\mu _ { 1 } > \mu _ { 2 }$

Essay

Test the hypothesis that $\mu _ { 1 } > \mu _ { 2 }$ . Two samples are randomly selected from each population. The sample statistics are given below. Use $\alpha = 0.01$ .
$$\begin{array} { l l } \mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 125 \\\overline { \mathrm { x } } 1 = 520 & \overline { \mathrm { x } } 2 = 505 \\\mathrm {~s} _ { 1 } = 45 & \mathrm {~s} _ { 2 } = 25\end{array}$$