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.
-A coach uses a new technique in training middle distance runners. The times for 9 different athletes to run 800 meters before and after this training are shown below.
$\begin{array}{r|ccccccccc}\text { Athlete } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } & \text { I } \\\hline \text { Time before training (seconds) } & 115.2 & 120.9 & 108.0 & 112.4 & 107.5 & 119.1 & 121.3 & 110.8 & 122.3 \\\hline \text { Time after training (seconds) } & 116.0 & 119.1 & 105.1 & 111.9 & 109.1 & 115.2 & 118.5 & 110.7 & 120.9\end{array}$

Construct a $99 \%$ confidence interval for the mean difference of the "before" minus "after" times.

A) $- 0.85 < \mu _ { \mathrm { d } } < 3.29$
B) $- 0.76 < \mu _ { \mathrm { d } } < 3.20$
C) $- 0.82 < \mu _ { \mathrm { d } } < 3.26$
D) $- 0.54 < \mu _ { \mathrm { d } } < 2.98$