Chi-square (X²) goodness-of-fit test

For a sample of N observations from a random variable x(k),

where

f_i = observed frequency

F_i = expected frequency

in the i^th class interval, respectively.

Hypothesis:

The variable x(k) has a probability p(x) = p₀(x).

Acceptance region:

where the value χ²_n;α is the chi-square statistic for a degree of freedom n = K - 3.