Use the Data in the Given Table and the Corresponding

question 155

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. $\begin{array}{l|lll} & \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } \\\hline \text { Car 1 } & 22.4 & 25.2 & 24.3 \\\text { Car 2 } & 19 & 18.6 & 19.8 \\\text { Car 3 } & 24.6 & 25 & 25.4 \\\text { Car 4 } & 23.5 & 23.6 & 24.1\end{array}$


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

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Definitions:

Confidence Interval

A range of values, derived from sample data, that is used to estimate the true value of a population parameter with a specified level of confidence.

Prediction Interval

In statistics, a range within which a future observation or data point is expected to fall, with a specified probability.

Heteroscedasticity

A condition in regression analysis where the variance of the error terms or disturbances is not constant across all levels of an independent variable.

Error Variable

A random variable signifying the discrepancy between the forecasted value and the true observed value in statistical analysis.