# Tail Areas under Chi-Squared Distributions

Tail Areas under Chi-Squared Distributions

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

2

χ

α

2

χ

r

2

χ

α

2

χ

1-α