The two data sets are dependent. Find $\bar { d }$ to the nearest tenth.
-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)$\sqrt{\frac{s_{1}^{2}}{n_{1}}-\frac{s_{2}^{2}}{n_{2}}}$

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

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

D)$\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}$

Question

The two data sets are dependent. Find $\bar { d }$ to the nearest tenth.
-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)$\sqrt{\frac{s_{1}^{2}}{n_{1}}-\frac{s_{2}^{2}}{n_{2}}}$

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

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

D)$\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}$

Quizplus · Accepted Answer

The population standard deviation of the difference in sample means, $\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right)$, for independent samples is given by $\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}$, where $s_1$ and $s_2$ are the sample standard deviations, and $n_1$ and $n_2$ are the sample sizes of the two samples, respectively.

The Two Data Sets Are Dependent dˉ\bar { d }dˉ To the Nearest Tenth

The Two Data Sets Are Dependent $\bar { d }$ To the Nearest Tenth