A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. Give an expression for the population standard deviation of the $\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right)$ values in terms of $\mathrm { s } _ { 1 } , \mathrm {~s} _ { 2 } , \mathrm { n } _ { 1 }$, and $\mathrm { n } _ { 2 }$.

A) $\sqrt { \frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm { n } _ { 1 } } + \frac { \mathrm { s } _ { 2 } ^ { 2 } } { \mathrm { n } _ { 2 } } }$

B) $\sqrt { \frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm { n } \frac { 2 } { 1 } } + \frac { \mathrm { s } 2 } { \mathrm { n } \frac { 2 } { 2 } } }$

C) $\sqrt { \frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm { n } _ { 1 } } - \frac { \mathrm { s } _ { 2 } ^ { 2 } } { \mathrm { n } _ { 2 } } }$

D) $\frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm { n } _ { 1 } } + \frac { \mathrm { s } _ { 2 } ^ { 2 } } { \mathrm { n } _ { 2 } }$

Question

A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. Give an expression for the population standard deviation of the

\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right)

values in terms of

\mathrm { s } _ { 1 } , \mathrm {~s} _ { 2 } , \mathrm { n } _ { 1 }

, and

\mathrm { n } _ { 2 }

.

A) $\sqrt { \frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm { n } _ { 1 } } + \frac { \mathrm { s } _ { 2 } ^ { 2 } } { \mathrm { n } _ { 2 } } }$

B) $\sqrt { \frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm { n } \frac { 2 } { 1 } } + \frac { \mathrm { s } 2 } { \mathrm { n } \frac { 2 } { 2 } } }$

C) $\sqrt { \frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm { n } _ { 1 } } - \frac { \mathrm { s } _ { 2 } ^ { 2 } } { \mathrm { n } _ { 2 } } }$

D) $\frac { \mathrm { s } _ { 1 } ^ { 2 } } { \mathrm { n } _ { 1 } } + \frac { \mathrm { s } _ { 2 } ^ { 2 } } { \mathrm { n } _ { 2 } }$

Quizplus · Accepted Answer

The population standard deviation of the $\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right)$ values is given by:$$\sigma_{\bar{x}_1 - \bar{x}_2} = \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$$where $\sigma_1^2$ and $\sigma_2^2$ are the population variances of the two populations, and $n_1$ and $n_2$ are the sample sizes.Since the sample sizes are large and the samples are independent, we can use the sample standard deviations, $s_1$ and $s_2$, to estimate the population standard deviations. Therefore, the population standard deviation of the $\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right)$ values is estimated by:$$\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$

A Hypothesis Test Is to Be Performed to Test the Equality