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) $\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}$

Question

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) $\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}$

Quizplus · Accepted Answer

The standard error of the difference between two independent sample means is given by the formula $\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}$.

If Two Random Samples of Sizes n1n _ { 1 }n1​

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