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:

- The curve is nonsymmetrical and skewed to the right.
- There is a different chi-square curve for each degree of freedom (
*df*). - The test statistic for any test is always greater than or equal to zero.
- When
*df*> 90, the chi-square curve approximates the normal distribution. - 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*

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