The standard error of the difference between sample means, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , is calculated by the formula $\sigma _ { \bar { x } _ { 1 } - \bar { x } _ { 2 } } = \sqrt { \sigma _ { 1 } ^ { 2 } / n _ { 1 } - \sigma _ { 2 } ^ { 2 } / n _ { 2 } }$ where $\sigma _ { i } ^ { 2 }$ is the variance of population i (i = 1, 2).

Question

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The correct formula for the standard error of the difference between sample means is $\sigma _ { \bar { x } _ { 1 } - \bar { x } _ { 2 } } = \sqrt { \sigma _ { 1 } ^ { 2 } / n _ { 1 } + \sigma _ { 2 } ^ { 2 } / n _ { 2 } }$, not subtraction.

The Standard Error of the Difference Between Sample Means Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​

The Standard Error of the Difference Between Sample Means $\bar { X } _ { 1 } - \bar { X } _ { 2 }$