The Student-t and the F-distributions have no relationship to each other.

Question

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The Student-t and the F-distributions are related as both are derived from the normal distribution and are used in hypothesis testing and confidence interval estimation, particularly in the context of small sample sizes or unknown population variances. The F-distribution is also used to compare variances between two samples, which can involve the square of a Student-t distributed variable.

The Student-T and the F-Distributions Have No Relationship to Each