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.

Probability density functions and X² values

• Acceptance region = X² < 51 at 5% significance level (i.e., accepted with a 95% probability)
• All data variables fail the test, i.e. not normally distributed.