Determine Whether the Samples Are Independent or Dependent Construct a 95% Confidence Interval For

Multiple Choice

Determine whether the samples are independent or dependent.
-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. $$\begin{array} { | c | c c | } \hline \text { College A } & { \text { College B } } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & & \\\hline\end{array}$$ Construct a 95% confidence interval for $$\mu _ { 1 } - \mu _ { 2 }$$ , 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) $- 0.75 < \mu _ { 1 } - \mu _ { 2 } < 0.10$
B) $- 0.78 < \mu _ { 1 } - \mu _ { 2 } < 0.13$
C) $- 0.81 < \mu _ { 1 } - \mu _ { 2 } < 0.15$
D) $- 0.70 < \mu _ { 1 } - \mu _ { 2 } < 0.05$