![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The interaction questions please (The last 3)
![**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](https://content.bartleby.com/qna-images/question/8ad87420-52d2-4e34-815e-eb9bcb5c95c0/095908fa-1010-4f0e-b853-939580284db7/xvhf27g_thumbnail.png)
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.](https://content.bartleby.com/qna-images/question/8ad87420-52d2-4e34-815e-eb9bcb5c95c0/095908fa-1010-4f0e-b853-939580284db7/y9nv33i_thumbnail.png)
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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