Answer
$χ2_{0.99} = 9.542$
$χ2_{0.025} = 40.289$
Work Step by Step
n = 23, df = n-1 = 22, Confidence level 98%
α = 1 - 0.98 = 0.02
α/2 = 0.01, 1 - α/2 = 0.99
Using table-VII of the book we have:
$χ2_{1-α/2} = χ2_{0.99} = 9.542$
$χ2_{α/2} = χ2_{0.025} = 40.289$