The Data for a Random Sample of Six Paired Observations $s d ^ { 2 }$

Essay

The data for a random sample of six 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 $s d ^ { 2 }$ .
b. Calculate the standard deviations $s _ { 1 } ^ { 2 }$ and $s _ { 2 } ^ { 2 }$ of each column of observations. Then find pooled estimate of the variance $s p ^ { 2 }$ .
c. Comparing $s d ^ { 2 }$ and $s p ^ { 2 }$ , explain the benefit of a paired difference experiment.