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Part 1
Find the critical values chi squared Subscript Upper L and chi squared Subscript Upper R for the given confidence level c and sample size n.
cequals0.98​,  nequals27
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Part 1
chi squared Subscript Upper Lequals
  
enter your response here ​(Round to three decimal places as​ needed.)

To find the critical values \(\chi^2_L\) and \(\chi^2_R\) for the given confidence level \(c = 0.98\) and sample size \(n = 27\), we need to use the chi-square distribution.

The degrees of freedom (df) for the chi-square distribution are:
\[
df = n - 1 = 27 - 1 = 26
\]

For a confidence level of \(c = 0.98\), the area in each tail of the chi-square distribution is \(\alpha = 1 - c = 0.02\). This means that the left tail has an area of \(\frac{\alpha}{2} = 0.01\), and the right tail has an area of \(\frac{\alpha}{2} = 0.01\).

To find the critical values \(\chi^2_L\) and \(\chi^2_R\):
- \(\chi^2_L\) corresponds to the 0.99 percentile of the chi-square distribution with 26 degrees of freedom.
- \(\chi^2_R\) corresponds to the 0.01 percentile of the chi-square distribution with 26 degrees of freedom.

Using a chi-square table or a calculator, we find the following:
\[
\chi^2_L = 13.844
\]
\[
\chi^2_R = 46.928
\]

Thus:
\[
\chi^2_L = 13.844 \quad \text{(rounded to three decimal places)}
\]
\[
\chi^2_R = 46.928 \quad \text{(rounded to three decimal places)}
\]

Would you like more details or have any questions?

Here are some follow-up questions:
1. How do we calculate degrees of freedom for different sample sizes?
2. What does the chi-square distribution represent in hypothesis testing?
3. How does the confidence level affect the critical values in the chi-square distribution?
4. Can you explain the significance of the left and right critical values?
5. What would happen to the critical values if the sample size were larger?

**Tip**: When using tables for critical values, it's important to round appropriately and make sure you're using the correct degrees of freedom for your sample size.

Find the critical values chi squared Subscript Upper L and chi squared Subscript Upper R for the given confidence level c and sample size n. c = 0.98, n = 27

Discover how to find critical chi-square values for a confidence level of 0.98 and a sample size of 27. This problem involves key concepts such as the chi-square distribution, degrees of freedom, and hypothesis testing, with step-by-step calculations provided for both left and right tail values.

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