Use the given information to find the number of degrees of​ freedom, the critical values 

chi Subscript Upper L Superscript 2χ2L 

and 

chi Subscript Upper R Superscript 2χ2R​, 

and the confidence interval estimate of 

sigmaσ. 

It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Nicotine in menthol cigarettes 

9090​% 

​confidence; 

nequals=2525​, 

sequals=0.280.28 

mg.

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Part 1

dfequals=2424 

​(Type a whole​ number.) 

Part 2

chi Subscript Upper L Superscript 2χ2Lequals=13.84813.848 

​(Round to three decimal places as​ needed.)

Part 3

chi Subscript Upper R Superscript 2χ2Requals=enter your response here 

​(Round to three decimal places as​ needed.)

### Part 1: Degrees of Freedom (df)
As already determined, the degrees of freedom (\(df\)) is:
\[
df = 25 - 1 = 24
\]

### Part 2: Critical Value \(\chi^2_L\)
From the chi-square table for 24 degrees of freedom and a left-tail area of \(\alpha/2 = 0.05\), the critical value \(\chi^2_L\) is:
\[
\chi^2_L = 13.848 \quad \text{(rounded to three decimal places)}
\]

### Part 3: Critical Value \(\chi^2_R\)
For the right-tail critical value \(\chi^2_R\), we use the area \(1 - \alpha/2 = 0.95\) for 24 degrees of freedom. From the chi-square table:
\[
\chi^2_R = 36.415 \quad \text{(rounded to three decimal places)}
\]

### Summary:
- Degrees of freedom (\(df\)): 24
- Critical value \(\chi^2_L\): 13.848
- Critical value \(\chi^2_R\): 36.415

Would you like to proceed with the confidence interval calculation for \(\sigma\)?

### 5 Related Questions:
1. What is the significance of the critical values in constructing the confidence interval?
2. How does the chi-square distribution differ from the normal distribution in this context?
3. How would the confidence interval change with a 95% confidence level?
4. Why do we use degrees of freedom when looking

Use the given information to find the number of degrees of freedom, the critical values chi Subscript Upper L Superscript 2χ2L and chi Subscript Upper R Superscript 2χ2R​, and the confidence interval estimate of sigmaσ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes, 90% confidence; n=25, s=0.28 mg.

Find the degrees of freedom, critical values (Chi-Square L and R), and confidence interval for the variance of nicotine content in menthol cigarettes using a 90% confidence level. This problem involves key statistical concepts such as chi-square distribution, degrees of freedom, and confidence intervals.

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