Math Problem Statement
Find the critical values chi squared Subscript Upper Lχ2L and chi squared Subscript Upper Rχ2R for the given confidence level c and sample size n. cequals=0.80.8, nequals=2525 Question content area bottom Part 1 chi squared Subscript Upper Lχ2Lequals=enter your response here (Round to three decimal places as needed.)
Solution
To find the critical values and for a given confidence level and sample size , we need to determine the critical points from the chi-square distribution.
Given:
- Confidence level
- Sample size
The degrees of freedom () is calculated as :
The confidence level of 0.8 corresponds to the middle 80% of the chi-square distribution. This means that 10% of the distribution is in each tail (since 100% - 80% = 20%, and this is divided equally between the two tails).
We need to find the critical values for the chi-square distribution at the lower 10% and upper 90% tails:
- is the 10th percentile (0.1 quantile).
- is the 90th percentile (0.9 quantile).
Using a chi-square distribution table or calculator for :
-
For the lower tail critical value ():
-
For the upper tail critical value ():
Using a chi-square calculator or table for :
- (rounded to three decimal places)
- (rounded to three decimal places)
Therefore:
Would you like more details or have any questions? Here are some related questions:
- How do you find the degrees of freedom for a chi-square test?
- What is the chi-square distribution used for?
- How do you interpret the critical values in a chi-square test?
- What are the properties of the chi-square distribution?
- How do you find the chi-square critical value using a statistical table?
- What is the relationship between confidence level and critical values in a chi-square test?
- How do changes in sample size affect the critical values in a chi-square test?
- What are the applications of the chi-square test in real-world scenarios?
Tip: Always double-check your calculations and use accurate tables or calculators to ensure precision in your statistical analysis.
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Math Problem Analysis
Mathematical Concepts
Chi-square Distribution
Statistical Inference
Formulas
Chi-square critical values calculation
Theorems
Chi-square distribution properties
Suitable Grade Level
Advanced
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