The Data for a Random Sample of Five Paired Observations $\bar { d }$

Essay

The data for a random sample of five paired observations are shown below.

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 $\mu _ { D }$ .