e-Statistics > 4480-5480 Probability and Statistics II

## Chi-square Distribution

The chi-square distribution has the number of degrees of freedom (df) = . The curve lies on the positive line, and its shape is skewed to the right particularly when df is small. The value at the quantile function is numerically obtained as follows:

Here has a chi-square distribution.

Chi-square distribution table contains the selected quantiles in a useful form of table.

First we obtain the -test statistic . Then we can calculate the p-value

so that the value belongs to the critical region if it is less than .