Question

A car company is testing a new type of tire. They want to determine the time to 60 mph from a full stop in light rain, light snow and dry conditions. They test out tires on five randomly selected cars from the lot. They want to know if the stopping distance is significantly different under the three conditions. What is the factor?

Answer 1

Answer:

For this case the factor would be:

Road conditions

Because we are testing a new type of tire in order to determine if the time to 60 mph from a full stop in light raing, ligth snow and dry conditions.

Step-by-step explanation:

Previous concepts

By definition a factor usually known as "the independent variable is an explanatory variable manipulated by the experimenter".

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

If we assume that we have $p$ groups and on each group from $j=1,\dots,p$ we have $n_j$ individuals on each group we can define the following formulas of variation:  

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

And we have this property

$SST=SS_{between}+SS_{within}$

Solution to the problem

For this case the factor would be:

Road conditions

Because we are testing a new type of tire in order to determine if the time to 60 mph from a full stop in light raing, ligth snow and dry conditions.

Th use 5 experimental units that are selected from the an specific lot. And they want to test is the stopping distance is significantly different.

And for this case we can use a one way ANOVA to test if the means are equal  in the 3 groups.