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 $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } \text {. Use } \alpha = 0.025$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 15 & \mathrm { n } _ { 2 } = 15 \\\overline { \mathrm { x } } _1 = 24.63 & \overline { \mathrm { x } } _2 = 27.18 \\\mathrm {~s} _ { 1 } = 2.9 & \mathrm {~s} _ { 2 } = 2.8\end{array}$$