Find the critical values x²₁ and x²R for the given confidence level c and sample size n. L c=0.8, n = 22 X²L² = (Round to three decimal places as needed.) X²R= (Round to three decimal places as needed.)
Find the critical values x²₁ and x²R for the given confidence level c and sample size n. L c=0.8, n = 22 X²L² = (Round to three decimal places as needed.) X²R= (Round to three decimal places as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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Question
![### Finding Critical Values for Chi-Square Distribution
To calculate confidence intervals for a population variance, we use the Chi-Square distribution. The critical values for the Chi-Square distribution are denoted as \( \chi^2_L \) and \( \chi^2_R \).
**Given:**
- Confidence Level \( c = 0.8 \)
- Sample Size \( n = 22 \)
Based on this information, we need to find the critical values \( \chi^2_L \) and \( \chi^2_R \).
#### Instructions:
1. **Determine Degrees of Freedom:**
The degrees of freedom (df) can be calculated as:
\[
df = n - 1 = 22 - 1 = 21
\]
2. **Find Critical Values from Chi-Square Table:**
Using the Chi-Square table, find the critical values for the given confidence level \( c \) and degrees of freedom \( df \).
3. **Adjust for Confidence Level:**
For a two-tailed test with confidence level \( c \):
\[
\alpha = 1 - c = 1 - 0.8 = 0.2
\]
Divide this significance level into two tails:
\[
\alpha/2 = 0.2/2 = 0.1
\]
4. **Locate Critical Values:**
For \( df = 21 \) and \( \alpha/2 = 0.1 \), find the corresponding critical values \( \chi^2_L \) and \( \chi^2_R \) from the Chi-Square distribution table.
### Inputs:
- \( \chi^2_L \):
\[
\text{Round to three decimal places as needed.}
\]
- \( \chi^2_R \):
\[
\text{Round to three decimal places as needed.}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac4255ba-2787-4b8b-b63d-664d949df058%2F5a19d6a4-f1f6-4c59-ba94-5bb60e5e2e96%2Fkha6rrdl_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding Critical Values for Chi-Square Distribution
To calculate confidence intervals for a population variance, we use the Chi-Square distribution. The critical values for the Chi-Square distribution are denoted as \( \chi^2_L \) and \( \chi^2_R \).
**Given:**
- Confidence Level \( c = 0.8 \)
- Sample Size \( n = 22 \)
Based on this information, we need to find the critical values \( \chi^2_L \) and \( \chi^2_R \).
#### Instructions:
1. **Determine Degrees of Freedom:**
The degrees of freedom (df) can be calculated as:
\[
df = n - 1 = 22 - 1 = 21
\]
2. **Find Critical Values from Chi-Square Table:**
Using the Chi-Square table, find the critical values for the given confidence level \( c \) and degrees of freedom \( df \).
3. **Adjust for Confidence Level:**
For a two-tailed test with confidence level \( c \):
\[
\alpha = 1 - c = 1 - 0.8 = 0.2
\]
Divide this significance level into two tails:
\[
\alpha/2 = 0.2/2 = 0.1
\]
4. **Locate Critical Values:**
For \( df = 21 \) and \( \alpha/2 = 0.1 \), find the corresponding critical values \( \chi^2_L \) and \( \chi^2_R \) from the Chi-Square distribution table.
### Inputs:
- \( \chi^2_L \):
\[
\text{Round to three decimal places as needed.}
\]
- \( \chi^2_R \):
\[
\text{Round to three decimal places as needed.}
\]
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