To find the critical value of χ² given the alternative hypothesis \( H_1: \sigma > 26.1 \), we need to determine the critical value from the χ² distribution for a one-tailed test at a significance level \( \alpha = 0.01 \) with \( n - 1 \) degrees of freedom.
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Degrees of Freedom: Since \( n = 9 \), the degrees of freedom \( df \) is: \[ df = n - 1 = 9 - 1 = 8 \]
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α Level: The critical value is found for \( \alpha = 0.01 \).
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Finding the Critical Value: We look up or use a chi-squared distribution table or calculator to find the value such that the area to the right is \( 0.01 \) for \( df = 8 \).
Using a chi-squared distribution table or appropriate software, we find:
- The critical value \( χ^2 \) for \( df = 8 \) at the 0.01 level is approximately \( 21.666 \).
Thus, the answer is: \[ \boxed{21.666} \]