15.58 The manager of an automobile repair shop is looking for a car battery that may troubleshoot the factors that shorten a car’s battery lifetime and ensure a longer battery life. Three car battery brands claim that their products have a longer life (in years) than others. To determine whether there is a significant difference between the brands, the manager randomly selected nine cars that have been using the car batteries from the respective brands, and the results are reported in the following table. Test the null hypothesis that there are no differences between the average lifetime of the three brands.

Source of Variation Sum of Squares Degrees of Freedom Between groups 2.8041 2 Within groups 15.0409 24 Total 17.845 26