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

question 69

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.

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Definitions:

Color

The aspect of things that is caused by differing qualities of light being reflected or emitted by them, perceivable by the human eye.

Pixels

The smallest units of a digital image, representing a single point of color.

Window Width

Window width refers to the horizontal dimension of a window or display screen, often expressed in pixels.