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

Multiple Choice

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:

A) $\sqrt { \left( \sigma _ { 1 } ^ { 2 } - \sigma _ { 2 } ^ { 2 } \right) / n _ { 1 } n _ { 2 } }$ .
B) $\sqrt { \left( \sigma _ { 1 } ^ { 2 } + \sigma _ { 2 } ^ { 2 } \right) / n _ { 1 } n _ { 2 } }$ .
C) $\sqrt { \frac { \sigma _ { 1 } ^ { 2 } } { n _ { 1 } } - \frac { \sigma _ { 2 } ^ { 2 } } { n _ { 2 } } }$ .
D) $\sqrt { \frac { \sigma _ { 1 } ^ { 2 } } { n _ { 1 } } + \frac { \sigma _ { 2 } ^ { 2 } } { n _ { 2 } } }$ .