Construct a Confidence Interval For $\mu _ { d }$ The Mean of the Differences D for the Population

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

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