MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Factorial Experiment Analysis** A factorial experiment involving two levels of Factor A and three levels of Factor B resulted in the following data: | | Factor B | |-------------|-----------------| | | Level 1 | Level 2 | Level 3 | | **Factor A** | | | | | Level 1 | 131 | 94 | 75 | | | 161 | 70 | 93 | | Level 2 | 129 | 123 | 120 | | | 99 | 101 | 136 | **Instructions:** Conduct a test for any significant main effects and any interaction, using α = 0.05. 1. **Calculate the Test Statistic for Factor A:** - Round your answer to two decimal places and enter it in the space provided. - [Input box] 2. **Calculate the p-value for Factor A:** - Round your answer to three decimal places and enter it in the space provided. - \( p\text{-value} = \) [Input box] 3. **State Your Conclusion About Factor A:** Choose the correct conclusion based on the calculated p-value: - ☐ Because the \( p\text{-value} > \alpha = 0.05 \), Factor A is significant. - ☐ Because the \( p\text{-value} > \alpha = 0.05 \), Factor A is not significant. - ☐ Because the \( p\text{-value} \leq \alpha = 0.05 \), Factor A is not significant. - ☐ Because the \( p\text{-value} \leq \alpha = 0.05 \), Factor A is significant. 4. **Calculate the Test Statistic for Factor B:** - Round your answer to two decimal places and enter it in the space provided. - [Input box] 5. **Calculate the p-value for Factor B:** - Round your answer to three decimal places and enter it in the space provided. - \( p\text{-value} = \) [Input box] **Graph/Diagram Explanation:** The table above represents the mean values obtained from a factorial experiment with two factors, A and B, each with different levels. Factor A has two levels, and Factor B has
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Transcribed Image Text:**Factorial Experiment Analysis** A factorial experiment involving two levels of Factor A and three levels of Factor B resulted in the following data: | | Factor B | |-------------|-----------------| | | Level 1 | Level 2 | Level 3 | | **Factor A** | | | | | Level 1 | 131 | 94 | 75 | | | 161 | 70 | 93 | | Level 2 | 129 | 123 | 120 | | | 99 | 101 | 136 | **Instructions:** Conduct a test for any significant main effects and any interaction, using α = 0.05. 1. **Calculate the Test Statistic for Factor A:** - Round your answer to two decimal places and enter it in the space provided. - [Input box] 2. **Calculate the p-value for Factor A:** - Round your answer to three decimal places and enter it in the space provided. - \( p\text{-value} = \) [Input box] 3. **State Your Conclusion About Factor A:** Choose the correct conclusion based on the calculated p-value: - ☐ Because the \( p\text{-value} > \alpha = 0.05 \), Factor A is significant. - ☐ Because the \( p\text{-value} > \alpha = 0.05 \), Factor A is not significant. - ☐ Because the \( p\text{-value} \leq \alpha = 0.05 \), Factor A is not significant. - ☐ Because the \( p\text{-value} \leq \alpha = 0.05 \), Factor A is significant. 4. **Calculate the Test Statistic for Factor B:** - Round your answer to two decimal places and enter it in the space provided. - [Input box] 5. **Calculate the p-value for Factor B:** - Round your answer to three decimal places and enter it in the space provided. - \( p\text{-value} = \) [Input box] **Graph/Diagram Explanation:** The table above represents the mean values obtained from a factorial experiment with two factors, A and B, each with different levels. Factor A has two levels, and Factor B has
### Analysis of Variance (ANOVA) for Factors #### Factor B Analysis 1. **Find the value of the test statistic for factor B.** - Instruction: Round your answer to two decimal places. 2. **Find the \( p \)-value for factor B.** - Instruction: Round your answer to three decimal places. - \( p \)-value = [Input Field] 3. **State your conclusion about factor B.** - Options: - ○ Because the \( p \)-value \( \leq \alpha = 0.05\), factor B is not significant. - ○ Because the \( p \)-value \( > \alpha = 0.05\), factor B is not significant. - ○ Because the \( p \)-value \( > \alpha = 0.05\), factor B is significant. - ○ Because the \( p \)-value \( \leq \alpha = 0.05\), factor B is significant. #### Interaction Between Factors A and B 4. **Find the value of the test statistic for the interaction between factors A and B.** - Instruction: Round your answer to two decimal places. 5. **Find the \( p \)-value for the interaction between factors A and B.** - Instruction: Round your answer to three decimal places. - \( p \)-value = [Input Field] 6. **State your conclusion about the interaction between factors A and B.** - Options: - ○ Because the \( p \)-value \( \leq \alpha = 0.05\), the interaction between factors A and B is significant. - ○ Because the \( p \)-value \( > \alpha = 0.05\), the interaction between factors A and B is not significant. - ○ Because the \( p \)-value \( > \alpha = 0.05\), the interaction between factors A and B is significant. - ○ Because the \( p \)-value \( \leq \alpha = 0.05\), the interaction between factors A and B is not significant.
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Transcribed Image Text:### Analysis of Variance (ANOVA) for Factors #### Factor B Analysis 1. **Find the value of the test statistic for factor B.** - Instruction: Round your answer to two decimal places. 2. **Find the \( p \)-value for factor B.** - Instruction: Round your answer to three decimal places. - \( p \)-value = [Input Field] 3. **State your conclusion about factor B.** - Options: - ○ Because the \( p \)-value \( \leq \alpha = 0.05\), factor B is not significant. - ○ Because the \( p \)-value \( > \alpha = 0.05\), factor B is not significant. - ○ Because the \( p \)-value \( > \alpha = 0.05\), factor B is significant. - ○ Because the \( p \)-value \( \leq \alpha = 0.05\), factor B is significant. #### Interaction Between Factors A and B 4. **Find the value of the test statistic for the interaction between factors A and B.** - Instruction: Round your answer to two decimal places. 5. **Find the \( p \)-value for the interaction between factors A and B.** - Instruction: Round your answer to three decimal places. - \( p \)-value = [Input Field] 6. **State your conclusion about the interaction between factors A and B.** - Options: - ○ Because the \( p \)-value \( \leq \alpha = 0.05\), the interaction between factors A and B is significant. - ○ Because the \( p \)-value \( > \alpha = 0.05\), the interaction between factors A and B is not significant. - ○ Because the \( p \)-value \( > \alpha = 0.05\), the interaction between factors A and B is significant. - ○ Because the \( p \)-value \( \leq \alpha = 0.05\), the interaction between factors A and B is not significant.
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