Find the critical values x2L and x2R that correspond to the given confidence level and sample size.
99%: n=23
To find the critical values x2L and x2R corresponding to a given confidence level and sample size, we need to use the chi-square distribution table.
Step 1: Determine the degrees of freedom (df).
For this problem, the degrees of freedom can be calculated using n - 1, where n is the sample size. So, for n = 23, the degrees of freedom would be 23 - 1 = 22.
Step 2: Find the critical values.
Since we want to find the critical values corresponding to a 99% confidence level, we need to find the corresponding values in the chi-square distribution table for a cumulative area of 0.01 on each tail.
Looking up the value in the chi-square distribution table with df = 22 and a cumulative area of 0.01 in one tail, we find:
x2L = 9.591
This is the critical value on the left tail.
Since the chi-square distribution is symmetric, the critical value on the right tail can be found by subtracting the critical value on the left tail from the total area of both tails:
Area of both tails = 1 - confidence level = 1 - 0.99 = 0.01
Therefore, x2R = x2L = 9.591.
Both critical values are the same for a 99% confidence level and a sample size of 23.