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. Also assume that the population standard deviations are equal ( $\left( \sigma _ { 1 } = \sigma _ { 2 } \right)$ , so that the standard error of the difference between means is obtained by pooling the sample variances .
-A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs.
$\begin{array}{c|cc}\text { College A } & \text { College B } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & &\end{array}$
Construct a $95 \%$ confidence interval for the difference between the mean GPA of college A students and the mean GPA of college B students.
(Note: $\bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , \mathrm {~s} _ { 1 } = 0.4357 , \mathrm {~s} _ { 2 } = 0.5485$ .)

A) $- 0.72 < \mu _ { 1 } - \mu _ { 2 } < 0.07$
B) $- 0.65 < \mu _ { 1 } - \mu _ { 2 } < - 0.01$
C) $- 0.81 < \mu _ { 1 } - \mu _ { 2 } < 0.15$
D) $- 0.91 < \mu _ { 1 } - \mu _ { 2 } < 0.25$