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Car Crash Tests Data Set 19 鈥淐ar Crash Tests鈥 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?

Short Answer

Expert verified

The following three conclusions can be drawn.

  • The interaction between the factors 鈥榝emur鈥 and 鈥榗ar size鈥 does not have a significant effect on the crash test loads.
  • The factor 鈥榝emur鈥 does not have a significant effect on the crash test loads.
  • The factor 鈥榗ar size鈥 does not have a significant effect on the crash test loads.

Step by step solution

01

Given information

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

The significance level is 0.05.

02

Test the interaction effect

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 鈥榝emur鈥 and 鈥榗ar size鈥 on the crash test loads.

The alternative hypothesis is as follows.

There is a significant effect of the interaction between the factors 鈥榝emur鈥 and 鈥榗ar size鈥 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 鈥榝emur鈥 and 鈥榗ar size鈥 has a significant effect on crash test loads.

03

Test the effect of the row factor

The null hypothesis to test the significance of the effect of the factor 鈥榝emur鈥 is as follows.


There is no significant effect of the factor 鈥榝emur鈥 on the crash test loads.

The alternative hypothesis is as follows.

There is a significant effect of the factor 鈥榝emur鈥 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 鈥榝emur鈥 has a significant effect on crash test loads.

04

Test the column factor

The null hypothesis to test the significance of the effect of the factor 鈥榗ar size鈥 is as follows.


There is no significant effect of the factor 鈥榗ar size鈥 on the crash test loads.

The alternative hypothesis is as follows.

There is a significant effect of the factor 鈥榗ar size鈥 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 鈥榗ar size鈥 has a significant effect on crash test loads.

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4.8

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