The standard error of the difference between means is given by
A) $\sqrt { \frac { \left( \sigma _ { 1 } \right) ^ { 2 } } { n _ { 1 } } + \frac { ( \sigma ) ^ { 2 } } { n _ { 2 } } }$
B) $\frac { \sigma _ { 1 } } { n _ { 1 } } + \frac { \sigma _ { 2 } } { n _ { 2 } }$
C) $\frac { \left( \sigma _ { 1 } \right) ^ { 2 } } { n _ { 1 } } + \frac { ( \sigma } { n _ { 2 } } L ^ { 2 }$
D) $\sqrt { \frac { \sigma _ { 1 } } { n _ { 1 } } + \frac { \sigma _ { 2 } } { n _ { 2 } } }$

Question

The standard error of the difference between means is given by 
A) $\sqrt { \frac { \left( \sigma _ { 1 } \right) ^ { 2 } } { n _ { 1 } } + \frac { ( \sigma ) ^ { 2 } } { n _ { 2 } } }$
B) $\frac { \sigma _ { 1 } } { n _ { 1 } } + \frac { \sigma _ { 2 } } { n _ { 2 } }$
C) $\frac { \left( \sigma _ { 1 } \right) ^ { 2 } } { n _ { 1 } } + \frac { ( \sigma } { n _ { 2 } } L ^ { 2 }$
D) $\sqrt { \frac { \sigma _ { 1 } } { n _ { 1 } } + \frac { \sigma _ { 2 } } { n _ { 2 } } }$

Quizplus · Accepted Answer

The formula for the standard error of the difference between means is given by A. It takes into account the sample sizes of both groups as well as their respective variances. Option B only includes the population standard deviations, but not the sample sizes. Option C includes a term for L which is not defined, and is also missing a square on the second standard deviation term. Option D is a simplified version of the formula but does not take into account the sample sizes.

The Standard Error of the Difference Between Means Is Given (σ1)2n1+(σ)2n2\sqrt { \frac { \left( \sigma _ { 1 } \right) ^ { 2 } } { n _ { 1 } } + \frac { ( \sigma ) ^ { 2 } } { n _ { 2 } } }n1​(σ1​)2​+n2​(σ)2​​

The Standard Error of the Difference Between Means Is Given $\sqrt { \frac { \left( \sigma _ { 1 } \right) ^ { 2 } } { n _ { 1 } } + \frac { ( \sigma ) ^ { 2 } } { n _ { 2 } } }$