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Tail Areas under Chi-Squared Distributions

​
tail area
0.05
degrees of freedom
10
Tail probabilities from various probability distributions are used in constructing confidence intervals and hypothesis tests in statistics. The symbol
2
χ
α
(r)
is the number such that the area under a
2
χ
probability distribution with
r
degrees of freedom to the right of
2
χ
α
(r)
is equal to α. Thus, this number is the left boundary of the right tail and the number
2
χ
1-α
(r)
is the right boundary of the left tail.
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