### Analysis of Variance (ANOVA) for Vehicle Size Categories in Crash TestsThis study examines data from crash tests for four different vehicle size categories (Small, Midsize, Large, and SUV), focusing on the measured amounts of left leg femur force (kN). Using a 0.05 significance level, we aim to determine if the four vehicle size categories have the same mean force on the femur of the left leg. The question is whether the size of the car affects the force on the left femur during crashes.#### ANOVA Table| Source | DF | Adj SS | Adj MS | F-Value | P-Value ||-----------|----|--------|--------|---------|---------|| Size | 3 | 0.7781 | 0.2427 | 0.63 | 0.599 || Error | 52 | 20.0304| 0.3852 | | || Total | 55 | 20.7655| | | |- **DF**: Degrees of Freedom- **Adj SS**: Adjusted Sum of Squares- **Adj MS**: Adjusted Mean SquareThe P-Value (0.599) indicates that there is not enough statistical evidence to reject the null hypothesis at a 0.05 significance level.#### Hypothesis Testing**Null Hypothesis (H₀):**- \( \mu_1 = \mu_2 = \mu_3 = \mu_4 \)- The means of femur force for all car size categories are equal.**Alternative Hypothesis (H₁):**- At least one of the means is different from the others.**Test Statistic:**- The calculated test statistic is \( F = 0.63 \).**Conclusion:**- Since the P-Value is greater than 0.05, we fail to reject the null hypothesis. There is no significant difference in the mean femur forces among the four vehicle size categories.This analysis indicates that vehicle size does not have a statistically significant effect on the left femur force during crashes at the 0.05 level.

The one-way Analysis of Variance output is given.

Answered: The data from car crash tests for four…

MATLAB: An Introduction with Applications

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Author:Amos Gilat

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