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.
-If $\overline { \mathrm { d } } = 3.125 , \mathrm {~S} _ { \mathrm { d } } = 2.911$ , and $\mathrm { n } = 8$ , determine a 90 percent confidence interval for $\mu _ { \mathrm { d } }$ .

A) $2.435 < \mu _ { \mathrm { d } } < 5.075$
B) $1.175 < \mu _ { \mathrm { d } } < 5.075$
C) $1.175 < \mu _ { \mathrm { d } } < 3.815$
D) $2.435 < \mu _ { \mathrm { d } } < 3.815$