Use the Data in the Given Table and the Corresponding

question 86

Essay

Use the data in the given table and the corresponding Minitab display to test the hypothesis.
The following table shows the mileage for four different cars and three different brands of
gas. Assuming no effect from the interaction between car and brand of gas, test the claim that
the four cars have the same mean mileage. Use a 0.05 significance level. $\begin{array}{l|lll} & \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } \\\hline \text { Car 1 } & 22.4 & 25.2 & 24.3 \\\text { Car 2 } & 19 & 18.6 & 19.8 \\\text { Car 3 } & 24.6 & 25 & 25.4 \\\text { Car 4 } & 23.5 & 23.6 & 24.1\end{array}$

$\begin{array}{lrcrrc}\text { Source } & D F & S S & M S & F & p \\\text { Car } & 3 & 61.249 & 20.416 & 39.033 & 0.000249 \\\text { Gas } & 2 & 2.222 & 1.111 & 2.124 & 0.200726 \\\text { Error } & 6 & 3.138 & 0.523 & & \\\text { Total } & 11 & 66.609 & & &\end{array}$

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Definitions:

Social Skills Training

A form of behavior therapy used to improve interpersonal skills through teaching, modeling, and practicing specific behaviors.

Powerlessness

A state of feeling unable to control one's own life or influence outcomes, often associated with situations of oppression or illness.

Personal Autonomy

The capacity to make an informed, uncoerced decision about one's own actions and life direction.

Instilling Hope

The process of encouraging optimism and a positive outlook in individuals, especially in therapeutic settings.