WOLFRAM|DEMONSTRATIONS PROJECT

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.