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

Essay

Test the claim that $\mu _ { 1 } \neq \mu _ { 2 }$ Two samples are random, independent, and come from populations that are
normally distributed. The sample statistics are given below. Assume that $$\sigma _ { 1 } ^ { 2 } \neq \sigma_{ 2 }^ { 2 } \text {. Use } \alpha = 0.02$$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\\overline { \mathrm { x } }_ 1 = 4 & \overline { \mathrm { x } } _2 = 4.4 \\\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 0.51\end{array}$$