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The data from car crash tests for four different vehicle size categories (Small, Midsize, Large, and SUV) with measured amounts of left leg femur force (kN) results in the following Minitab display. Using a 0.05 significance level, test the claim that the four vehicle size categories have the same mean force on the femur of the left leg. Does size of the car appear to have an effect on the force on the left femur in crash tests? Analysis of Variance Source Size Error Total DF 3 56 59 Adj SS 0.6657 22.1872 22.8529 Adj MS 0.2219 0.3962 F-Value 0.56 P-Value 0.644

The data from car crash tests for four different vehicle size categories (Small, Midsize, Large, and SUV) with measured amounts of left leg femur force (kN) results in the following Minitab display. Using a 0.05 significance level, test the claim that the four vehicle size categories have the same mean force on the femur of the left leg. Does size of the car appear to have an effect on the force on the left femur in crash tests? Analysis of Variance Source Size Error Total DF 3 56 59 Adj SS 0.6657 22.1872 22.8529 Adj MS 0.2219 0.3962 F-Value 0.56 P-Value 0.644

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Analysis of Vehicle Size Categories on Crash Test Results** The data from car crash tests for four different vehicle size categories (Small, Midsize, Large, and SUV) include measurements of the left leg femur force in kilonewtons (kN) and are summarized in the following Minitab display. The goal is to test whether the four vehicle size categories have the same mean force on the femur of the left leg using a significance level of 0.05. We aim to determine if the size of the vehicle impacts the force experienced by the left femur during crashes. **Analysis of Variance (ANOVA) Results:** | Source | DF | Adj SS | Adj MS | F-Value | P-Value | |--------|----|---------|---------|---------|---------| | Size | 3 | 0.6657 | 0.2219 | 0.56 | 0.644 | | Error | 56 | 22.1872 | 0.3962 | | | | Total | 59 | 22.8529 | | | | **Explanation of the Table:** - **DF (Degrees of Freedom):** Represents the number of values free to vary. For the size categories, DF is 3, and for the error, it is 56, with a total of 59. - **Adj SS (Adjusted Sum of Squares):** Represents the variation attributed to each source. For the size category, it's 0.6657, and for the error, it is 22.1872. - **Adj MS (Adjusted Mean Square):** Obtained by dividing the Adj SS by the corresponding DF. The values are 0.2219 for size and 0.3962 for error. - **F-Value:** The ratio of the mean square of the size category to the mean square of the error, here calculated as 0.56. - **P-Value:** This value is 0.644, which is greater than the significance level of 0.05. **Conclusion:** Since the P-Value (0.644) is greater than the significance level of 0.05, we do not reject the null hypothesis. Therefore, there is no statistically significant effect of vehicle size on the mean force experienced by the left femur in crash tests.
Transcribed Image Text:**Analysis of Vehicle Size Categories on Crash Test Results** The data from car crash tests for four different vehicle size categories (Small, Midsize, Large, and SUV) include measurements of the left leg femur force in kilonewtons (kN) and are summarized in the following Minitab display. The goal is to test whether the four vehicle size categories have the same mean force on the femur of the left leg using a significance level of 0.05. We aim to determine if the size of the vehicle impacts the force experienced by the left femur during crashes. **Analysis of Variance (ANOVA) Results:** | Source | DF | Adj SS | Adj MS | F-Value | P-Value | |--------|----|---------|---------|---------|---------| | Size | 3 | 0.6657 | 0.2219 | 0.56 | 0.644 | | Error | 56 | 22.1872 | 0.3962 | | | | Total | 59 | 22.8529 | | | | **Explanation of the Table:** - **DF (Degrees of Freedom):** Represents the number of values free to vary. For the size categories, DF is 3, and for the error, it is 56, with a total of 59. - **Adj SS (Adjusted Sum of Squares):** Represents the variation attributed to each source. For the size category, it's 0.6657, and for the error, it is 22.1872. - **Adj MS (Adjusted Mean Square):** Obtained by dividing the Adj SS by the corresponding DF. The values are 0.2219 for size and 0.3962 for error. - **F-Value:** The ratio of the mean square of the size category to the mean square of the error, here calculated as 0.56. - **P-Value:** This value is 0.644, which is greater than the significance level of 0.05. **Conclusion:** Since the P-Value (0.644) is greater than the significance level of 0.05, we do not reject the null hypothesis. Therefore, there is no statistically significant effect of vehicle size on the mean force experienced by the left femur in crash tests.
### Hypothesis Testing for Vehicle Size and Crash Test Force #### Determine the null hypothesis: - \( H_0: \) [Dropdown menu] #### Determine the alternative hypothesis: - \( H_1: \) [Dropdown menu] #### Determine the test statistic: - The test statistic is \([Empty box]\). *(Round to two decimal places as needed.)* #### Determine the P-value: - The P-value is \([Empty box]\). *(Round to three decimal places as needed.)* --- #### Decision Making: - The P-value is \([Empty box]\). *(Round to three decimal places as needed.)* - Does size of the car appear to have an effect on the force on the left femur in crash tests? \([Dropdown menu]\) \( H_0: \) There \([Dropdown menu]\) sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the four vehicle size categories have the same mean force on the left femur in crash tests. This structure outlines a statistical analysis framework for determining the effect of car size on crash test outcomes, specifically focusing on the force on the left femur. The process involves selecting hypotheses, calculating test statistics, and determining P-values before making a conclusion based on the evidence.
Transcribed Image Text:### Hypothesis Testing for Vehicle Size and Crash Test Force #### Determine the null hypothesis: - \( H_0: \) [Dropdown menu] #### Determine the alternative hypothesis: - \( H_1: \) [Dropdown menu] #### Determine the test statistic: - The test statistic is \([Empty box]\). *(Round to two decimal places as needed.)* #### Determine the P-value: - The P-value is \([Empty box]\). *(Round to three decimal places as needed.)* --- #### Decision Making: - The P-value is \([Empty box]\). *(Round to three decimal places as needed.)* - Does size of the car appear to have an effect on the force on the left femur in crash tests? \([Dropdown menu]\) \( H_0: \) There \([Dropdown menu]\) sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the four vehicle size categories have the same mean force on the left femur in crash tests. This structure outlines a statistical analysis framework for determining the effect of car size on crash test outcomes, specifically focusing on the force on the left femur. The process involves selecting hypotheses, calculating test statistics, and determining P-values before making a conclusion based on the evidence.
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