The Data for a Random Sample of Six Paired Observations

question 5

Essay

The data for a random sample of six paired observations are shown below. $\begin{array} { l c c } \text { Pair } & \text { Observation 1 } & \text { Observation 2 } \\ 1 & 1 & 3 \\ 2 & 2 & 4 \\ 3 & 3 & 5 \\ 4 & 4 & 6 \\ 5 & 5 & 7 \\ 6 & 6 & 8 \end{array}$

a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1 . Use the differences to calculate $s ^ { 2 }$ .
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.

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Definitions:

Cellulose

A complex carbohydrate or polysaccharide that forms the primary structural component of plant cell walls.

Phospholipids

A type of lipid molecule that is a major component of all cell membranes, known for its structure with a hydrophobic tail and a hydrophilic head.

Dipeptide

A molecule consisting of two amino acids joined by a single peptide bond.

Dehydration Reaction

A chemical reaction in which two molecules are joined together with the removal of water, common in the synthesis of organic compounds.