The Data for a Random Sample of Five Paired Observations

The data for a random sample of five paired observations are shown below. $\begin{array}{lcc}\text { Pair } & \text { Observation 1 } & \text { Observation 2 } \\1 & 3 & 5 \\2 & 4 & 4 \\3 & 3 & 4 \\4 & 2 & 5 \\5 & 5 & 6\end{array}$

a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1 .
Use the differences to calculate $\bar { d }$ and $s _ { d }$ .
b. Calculate the means $\bar { x } _ { 1 }$ and $\bar { x } _ { 2 }$ of each column of observations. Show that $\bar { d } = \bar { x } _ { 1 } - \bar { x } _ { 2 }$ .
c. Form a $90 \%$ confidence interval for $\mu _ { D }$ .