Construct the Indicated Confidence Interval for the Difference Between the Two

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.
-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) .
$\begin{array}{c|rr}\text { Female } & \text { Male } & \\\hline 495 & 722 & 518 \\760 & 562 & 904 \\556 & 880 & 1150 \\904 & 520 & 805 \\520 & 500 & 480 \\1005 & 1250 & 970 \\743 & 750 & 605 \\660 & 1640 &\end{array}$
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.
(Note: $\bar { x } _ { 1 } = \$ 705.38 , \bar { x } _ { 2 } = \$ 817.07 , \mathrm {~s} _ { 1 } = \$ 183.86 , \mathrm {~s} _ { 2 } = \$ 330.15$ .

A) $- \$ 383 < \mu _ { 1 } - \mu _ { 2 } < \$ 159$
B) $- \$ 382 < \mu _ { 1 } - \mu _ { 2 } < \$ 158$
C) $- \$ 431 < \mu _ { 1 } - \mu _ { 2 } < \$ 208$
D) $- \$ 385 < \mu _ { 1 } - \mu _ { 2 } < \$ 164$