The Data for a Random Sample of Five Paired Observations

question 27

Essay

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

---

Definitions:

Electrical System

A network of electrical components deployed to generate, transmit, and distribute electricity to various endpoints.

Societal Responsibility

The obligation of organizations to act in ways that benefit society at large, beyond their own interests or profitability.

Ecological Environment

The complex of biological, chemical, and physical factors that act upon an organism or an ecological community and ultimately determine its form and survival.

General Public

The larger community of people in society who are not segmented by any specific interest or profession; the broad population.