$$\bar { x } _ { 1 } - \bar { x } _ { 2 } \text { is an unbiased statistic used to estimate } \mu _ { 1 } - \mu _ { 2 } \text {. }$$ $$\text { For two independent samples, } \sigma _ { \bar { x } _ { 1 } - \bar { x } _ { 2 } } = \sqrt { \frac { \sigma _ { 1 } ^ { 2 } } { n _ { 1 } } - \frac { \sigma _ { 2 } ^ { 2 } } { n _ { 2 } } } \text {. }$$

Question

Quizplus · Accepted Answer

This is a true statement. $\bar{x}_1-\bar{x}_2$ is an unbiased estimator of $\mu_1-\mu_2$, and the standard deviation of this estimator is given by $\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$. However, if the samples are assumed to have equal variances $\sigma_1^2=\sigma_2^2=\sigma^2$, this reduces to the expression given in the statement.

xˉ1−xˉ2 is an unbiased statistic used to estimate μ1−μ2. \bar { x } _ { 1 } - \bar { x } _ { 2 } \text { is an unbiased statistic used to estimate } \mu _ { 1 } - \mu _ { 2 } \text {. }xˉ1​−xˉ2​ is an unbiased statistic used to estimate μ1​−μ2​.

$\bar { x } _ { 1 } - \bar { x } _ { 2 } \text { is an unbiased statistic used to estimate } \mu _ { 1 } - \mu _ { 2 } \text {. }$