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

Essay

Test the claim that $\mu _ { 1 } > \mu _ { 2 }$ Two samples are random, independent, and come from populations that are
normally distributed. The sample statistics are given below. Assume that $\sigma { } _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 }$ . Use $\alpha$ = 0.01. $$\begin{array} { l l } \mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \\\overline { \mathrm { x } }_ 1 = 520 & \overline { \mathrm { x } _ { 2 } } = 505 \\\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25\end{array}$$