If Two Random Samples of Sizes $n _ { 1 }$

Short Answer

If two random samples of sizes $n _ { 1 }$ and $n _ { 2 }$ are selected independently from two populations with variances $\sigma _ { 1 } ^ { 2 }$ and $\sigma _ { 2 } ^ { 2 }$ , then the standard error of the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , equals: $\begin{array}{|l|l|}\hline A&\sqrt{\left(\sigma_{1}^{2}-\sigma_{2}^{2}\right) / n_{1} n_{2}} .\\\hline B&\sqrt{\left(\sigma_{1}^{2}+\sigma_{2}^{2}\right) / n_{1} n_{2}} .\\\hline C&\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}-\frac{\sigma_{2}^{2}}{n_{2}}}\\\hline D&\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}} .\\\hline \end{array}$