Car Crash Tests Data Set 19 “Car Crash Tests” in Appendix B lists results from car crash tests. The data set includes crash test loads (pounds) on the left femur and right femur. When those loads are partitioned into the three car size categories of small, midsize, and large, the two-way analysis of results from XLSTAT are as shown below. (The row factor of femur has the two values of left femur and right femur, and the column factor of size has the three values of small, midsize, and large.) Use a 0.05 significance level to apply the methods of two-way analysis of variance. What do you conclude?

Data are given on the crash test loads (pounds) classified under two categories: femur and car size.

The significance level is 0.05.

The null hypothesis to test the significance of the interaction effect is

\({H_0}:{\mu _1} = {\mu _2} = {\mu _3}\).

There is no significant effect of the interaction between the factors ‘femur’ and ‘car size’ on the crash test loads.

The alternative hypothesis is as follows.

There is a significant effect of the interaction between the factors ‘femur’ and ‘car size’ on the crash test loads.

The p-value corresponding to the F-statistic value of 1.7171 (under interaction) is equal to 0.1940.

As the p-value is greater than 0.05, the null hypothesis is failed to be rejected.

Thus, there is no sufficient evidence to conclude that the interaction between ‘femur’ and ‘car size’ has a significant effect on crash test loads.

The null hypothesis to test the significance of the effect of the factor ‘femur’ is as follows.

There is no significant effect of the factor ‘femur’ on the crash test loads.

The alternative hypothesis is as follows.

There is a significant effect of the factor ‘femur’ on the crash test loads.

The p-value corresponding to the F-statistic value of 1.3896 (under femur) is equal to 0.2462.

As the p-value is greater than 0.05, the null hypothesis is failed to be rejected.

Thus, there is no sufficient evidence to conclude that the factor ‘femur’ has a significant effect on crash test loads.

The null hypothesis to test the significance of the effect of the factor ‘car size’ is as follows.

There is no significant effect of the factor ‘car size’ on the crash test loads.

The alternative hypothesis is as follows.

There is a significant effect of the factor ‘car size’ on the crash test loads.

The p-value corresponding to the F-statistic value of 2.2296 (under femur) is equal to 0.1222.

As the p-value is greater than 0.05, the null hypothesis is failed to reject.

Thus, there is no sufficient evidence to conclude that the factor ‘car size’ has a significant effect on crash test loads.