Construct a Confidence Interval for µD, the Mean of the Differences

Multiple Choice

Construct a confidence interval for µd, 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. $\begin{array}{llllllllllll}\text { Before } & 33 & 33 & 38 & 33 & 35 & 35 & 40 & 40 & 40 & 31 \\\hline \text { After } & 34 & 28 & 25 & 28 & 35 & 33 & 31 & 28 & 35 & 33\end{array}$

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