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.
-A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a 95% confidence interval for the mean difference between the before and after scores. $\begin{array}{llllllllllll}\text { Before } & 74 & 83 & 75 & 88 & 84 & 63 & 93 & 84 & 91 & 77 \\\hline \text { After } & 73 & 77 & 70 & 77 & 74 & 67 & 95 & 83 & 84 & 75\end{array}$

A) $1.0 < \mu _ { \mathrm { d } } < 6.4$
B) $0.2 < \mu _ { \mathrm { d } } < 7.2$
C) $1.2 < \mu _ { \mathrm { d } } < 5.7$
D) $0.8 < \mu _ { \mathrm { d } } < 6.6$