Construct a Confidence Interval For $\mu _ { d }$ , the Mean of the Differences

Multiple Choice

Construct a confidence interval for $\mu _ { d }$ , the mean of the differences $d$ for the population of paired data. Assume that the population of paired differences is normally distributed. A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a $99 \%$ confidence interval for the mean difference between the before and after scores.
$\begin{array}{llllllllllll}\text { Before }&70 & 80 & 92 & 99 & 93 & 97 & 76 & 63 & 68 & 71 & 74 \\\hline \text { After } & 69 & 79 & 90 & 96 & 91 & 95 & 75 & 64 & 62 & 64 & 76\end{array}$

A) $- 0.5 < \mu _ { d } < 4.5$
B) $- 0.2 < \mu _ { d } < 4.2$
C) $- 0.1 < \mu _ { d } < 4.1$
D) $1.2 < \mu _ { d } < 2.8$