How does one determine if bingo numbers are evenly distributed or if some numbers occurred with a greater frequency? Or if the types of movies people preferred were different across different age groups or if a coffee machine dispensed approximately the same amount of coffee each time. These questions can be addressed by conducting a hypothesis test. One distribution that can be used to find answers to such questions is known as the chi-square distribution. The chi-square distribution has applications in tests for independence, goodness-of-fit tests, and test of a single variance.

The properties of the chi-square distribution are as follows:

1. The curve is nonsymmetrical and skewed to the right.
2. There is a different chi-square curve for each degree of freedom (df).
3. The test statistic for any test is always greater than or equal to zero.
4. When df > 90, the chi-square curve approximates the normal distribution.
5. The mean, μ, is located just to the right of the peak.

This text is adapted from 11.1 Facts About the Chi-Square Distribution - Introductory Statistics OpenStax