In a chi-square goodness-of-fit test, a sample of n observations has n - 1 degrees of freedom.

Name: In a chi-square goodness-of-fit test, a sample of n observations has n - 1 degrees of freedom.
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In a chi-square goodness-of-fit test, the number of degrees of freedom is equal to the number of categories minus 1. It does not depend on the sample size. So, if a test has n categories, the degrees of freedom will be n - 1.

In a Chi-Square Goodness-Of-Fit Test, a Sample of N Observations