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.
-Using the sample paired data below, construct a $90 \%$ confidence interval for the population mean of all differences $x - y$ .
$\begin{array}{c|ccccc}\mathrm{x} & 5.0 & 5.1 & 4.6 & 3.5 & 6.0 \\\hline \mathrm{y} & 4.7 & 3.9 & 4.2 & 4.2 & 3.7\end{array}$

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