Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

Multiple Choice

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-Ten different families are tested for the number of gallons of water a day they use before and after viewing a conservation video. Construct a $90 \%$ confidence interval for the mean of the differences.
$\begin{array}{lllllllllll}\text { Before } & 33 & 33 & 38 & 33 & 35 & 35 & 40 & 40 & 40 & 31 \\\hline \text { After } & 34 & 28 & 25 & 28 & 35 & 33 & 31 & 28 & 35 & 33\end{array}$

A) $1.5 < \mu _ { \mathrm { d } } < 8.1$
B) $3.8 < \mu _ { \mathrm { d } } < 5.8$
C) $1.8 < \mu _ { \mathrm { d } } < 7.8$
D) $2.5 < \mu _ { \mathrm { d } } < 7.1$