For an F distribution test statistic, the number of degrees of freedom associated with its denominator can be larger, smaller, or equal to the number of degrees of freedom associated with its numerator.

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This is true. The F distribution is a ratio of two chi-square distributions, with the numerator typically representing the variability between groups or factors, and the denominator representing the variability within groups or error. Therefore, the number of degrees of freedom in the denominator can be larger, smaller, or equal to the number of degrees of freedom in the numerator.

For an F Distribution Test Statistic, the Number of Degrees