Find the critical values x1-a/2 and x12 for a 80% confidence level and a sample size of n = 10. X1-a/2 =U (Round to three decimal places as needed.) (Round to three decimal places as needed.)
Find the critical values x1-a/2 and x12 for a 80% confidence level and a sample size of n = 10. X1-a/2 =U (Round to three decimal places as needed.) (Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![### Finding Critical Values for Chi-Square Distribution
In this exercise, you will determine the critical values \(\chi^2_{1-\alpha/2}\) and \(\chi^2_{\alpha/2}\) for an 80% confidence level and a sample size of \(n = 10\).
#### Critical Value Calculation
To find the critical values, you need to refer to the chi-square distribution table and use the following formulas:
\[ \chi^2_{1-\alpha/2} = \_ \]
(Round to three decimal places as needed.)
\[ \chi^2_{\alpha/2} = \_ \]
(Round to three decimal places as needed.)
Given:
- Confidence Level: 80%
- Sample Size: \(n = 10\)
### Steps:
1. **Determine \(\alpha\)**:
Since the confidence level is 80%, \(\alpha = 1 - 0.80 = 0.20\).
2. **Identify \(\alpha/2\) and \(1-\alpha/2\)**:
- \(\alpha/2 = 0.20 / 2 = 0.10\)
- \(1 - \alpha/2 = 1 - 0.10 = 0.90\)
3. **Degrees of Freedom (df)**:
The degrees of freedom (df) is given by the formula \(df = n - 1\).
Here, \(df = 10 - 1 = 9\).
4. **Use Chi-Square Distribution Table**:
You will look up the critical values in the chi-square distribution table for df = 9 with \(\alpha/2 = 0.10\) and \(1 - \alpha/2 = 0.90\).
- \(\chi^2_{1-\alpha/2} = \text{Critical value at 0.90 for df = 9}\)
- \(\chi^2_{\alpha/2} = \text{Critical value at 0.10 for df = 9}\)
### Conclusion:
After determining the appropriate values from the chi-square table, you will have:
- \(\chi^2_{1-\alpha/2} = \_\_\_\)
- \(\chi^2_{\alpha/2} = \_\_\_\)
Remember to round your final answers to three decimal](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F240ac775-9f02-4c90-873e-56631fdfab69%2F1647b54f-d5ef-494c-bfb9-58e2fa47072e%2F3fkt8f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding Critical Values for Chi-Square Distribution
In this exercise, you will determine the critical values \(\chi^2_{1-\alpha/2}\) and \(\chi^2_{\alpha/2}\) for an 80% confidence level and a sample size of \(n = 10\).
#### Critical Value Calculation
To find the critical values, you need to refer to the chi-square distribution table and use the following formulas:
\[ \chi^2_{1-\alpha/2} = \_ \]
(Round to three decimal places as needed.)
\[ \chi^2_{\alpha/2} = \_ \]
(Round to three decimal places as needed.)
Given:
- Confidence Level: 80%
- Sample Size: \(n = 10\)
### Steps:
1. **Determine \(\alpha\)**:
Since the confidence level is 80%, \(\alpha = 1 - 0.80 = 0.20\).
2. **Identify \(\alpha/2\) and \(1-\alpha/2\)**:
- \(\alpha/2 = 0.20 / 2 = 0.10\)
- \(1 - \alpha/2 = 1 - 0.10 = 0.90\)
3. **Degrees of Freedom (df)**:
The degrees of freedom (df) is given by the formula \(df = n - 1\).
Here, \(df = 10 - 1 = 9\).
4. **Use Chi-Square Distribution Table**:
You will look up the critical values in the chi-square distribution table for df = 9 with \(\alpha/2 = 0.10\) and \(1 - \alpha/2 = 0.90\).
- \(\chi^2_{1-\alpha/2} = \text{Critical value at 0.90 for df = 9}\)
- \(\chi^2_{\alpha/2} = \text{Critical value at 0.10 for df = 9}\)
### Conclusion:
After determining the appropriate values from the chi-square table, you will have:
- \(\chi^2_{1-\alpha/2} = \_\_\_\)
- \(\chi^2_{\alpha/2} = \_\_\_\)
Remember to round your final answers to three decimal
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