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

question 29

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) \(\sqrt { \frac { \sigma _ { 1 } ^ { 2 } } { n _ { 1 } } + \frac { \sigma _ { 2 } ^ { 2 } } { n _ { 2 } } }\) .

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