When performing a two-tailed test,the lower-tailed critical value of the F distribution with n₁ - 1 degrees of freedom in the numerator and n₂ - 1 degrees of freedom in the denominator is exactly equivalent to the reciprocal of the upper-tailed critical value of the F distribution with n₂ - 1 degrees of freedom in the numerator and n₁ - 1 degrees of freedom in the denominator.

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Quizplus · Accepted Answer

This is a true statement based on the properties of the F distribution. The F distribution is a right-skewed distribution that has two critical values, one for the upper tail and one for the lower tail. The lower-tailed critical value of the F distribution with n₁ - 1 degrees of freedom in the numerator and n₂ - 1 degrees of freedom in the denominator is equal to the reciprocal of the upper-tailed critical value of the F distribution with n₂ - 1 degrees of freedom in the numerator and n₁ - 1 degrees of freedom in the denominator. This is because the F distribution is symmetric about its mean, which is equal to 1. Therefore, the critical values for the upper and lower tails are the same distance from the mean and are reciprocals of each other.

When Performing a Two-Tailed Test,the Lower-Tailed Critical Value of the F