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:

Summary Statistics

Statistical measures that capture important aspects of a dataset, such as its center, spread, and shape, with values like mean, median, and standard deviation.

Upper Fence

A value in boxplot analysis, calculated to identify outliers; it is typically set at Q3 + 1.5*IQR (where Q3 is the third quartile and IQR is the interquartile range).

Box And Whisker Plot

A graphical representation of data that shows the distribution's shape, central value, and variability.

Percentile

A measure indicating the value below which a given percentage of observations in a group falls.