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.
-Using the sample paired data below, construct a 90% confidence interval for the population mean of all differences x - y. $$\begin{array} { c | c c c c c } \mathrm { x } & 6.0 & 4.5 & 4.8 & 2.5 & 6.3 \\\hline \mathrm { y } & 5.7 & 3.3 & 4.4 & 3.2 & 4.0\end{array}$$

A) $- 0.37 < \mu _ { \mathrm { d } } < 1.77$
B) $0.22 < \mu _ { \mathrm { d } } < 7.48$
C) $- 0.31 < \mu _ { \mathrm { d } } < 1.71$
D) $- 0.07 < \mu _ { \mathrm { d } } < 1.47$