Determine whether the samples are independent or dependent.
-A researcher was interested in comparing the salaries of female and male employees at a particular company. Independent simple random samples of 8 female employees and 15 male employees yielded the following
Weekly salaries (in dollars). $$\begin{array} { r | r r }
\text { Female } & \text { Male } & \
\hline 495 & 722 & 518 \
760 & 562 & 904 \
556 & 880 & 1150 \
904 & 520 & 805 \
520 & 500 & 480 \
1005 & 1250 & 970 \
743 & 750 & 605 \
660 & 1640 &
\end{array}$$
Construct a 98% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ the difference between the mean weekly salary of female Employees and the mean weekly salary of male employees at the company. $\left( \text { Note: } \bar { x } _ { 1 } = \$ 705.38 , \bar { x } _ { 2 } = \$ 817.07 , \mathrm {~s} _ { 1 } = \$ 183.86 , \mathrm {~s} 2 = \$ 330.15 . \right)$
A) $- \$ 385

Question

Determine whether the samples are independent or dependent.
-A researcher was interested in comparing the salaries of female and male employees at a particular company. Independent simple random samples of 8 female employees and 15 male employees yielded the following
Weekly salaries (in dollars). $$\begin{array} { r | r r } 
\text { Female } & \text { Male } & \
\hline 495 & 722 & 518 \
760 & 562 & 904 \
556 & 880 & 1150 \
904 & 520 & 805 \
520 & 500 & 480 \
1005 & 1250 & 970 \
743 & 750 & 605 \
660 & 1640 &
\end{array}$$ 
Construct a 98% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ the difference between the mean weekly salary of female Employees and the mean weekly salary of male employees at the company. $\left( \text { Note: } \bar { x } _ { 1 } = \$ 705.38 , \bar { x } _ { 2 } = \$ 817.07 , \mathrm {~s} _ { 1 } = \$ 183.86 , \mathrm {~s} 2 = \$ 330.15 . \right)$
A) $- \$ 385 < \mu _ { 1 } - \mu _ { 2 } < \$ 164$
B) $- \$ 431 < \mu _ { 1 } - \mu _ { 2 } < \$ 208$
C) $- \$ 383 < \mu _ { 1 } - \mu _ { 2 } < \$ 159$
D) $- \$ 382 < \mu _ { 1 } - \mu _ { 2 } < \$ 158$

Quizplus · Accepted Answer

The samples are independent because the salary of one employee does not affect the salary of another employee. The confidence interval is:$$(\bar{x}_1 - \bar{x}_2) \pm t^* \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$where $t^*$ is the critical value from the t-distribution with $n_1 + n_2 - 2$ degrees of freedom and a significance level of 0.02 (since we want a 98% confidence interval).Plugging in the values, we get:$$(705.38 - 817.07) \pm 2.626 \sqrt{\frac{183.86^2}{8} + \frac{330.15^2}{15}}$$$$= -111.69 \pm 110.35$$$$= (-382.04, 158.36)$$Therefore, the correct answer is D.

Determine Whether the Samples Are Independent or Dependent Construct a 98% Confidence Interval For