Question

Which of the following statements is false for an F distribution? ​ a. Degrees of freedom for the numerator can be smaller than the degrees of freedom for the denominator. b. The exact shape of the distribution is determined by two numbers of degrees of freedom. c. Degrees of freedom for the numerator can be larger or equal to the degrees of freedom for the denominator. d. Degrees of freedom for the denominator cannot be smaller than the degrees of freedom for the numerator. e. Variables that are F distributed range from 0 to .

Answer 1

A. True

B. True

C. True

D. False

Explanation:

Option D is the only clear option that is false.

The S distribution is a statistical tool used to check the homogeneity of two independent estimates when studying population variance.

When using an F distribution, The ratio of the degree of freedom of the numerator to the denominator can be >1, = 1 or < 1.

This implies that degrees of freedom for the denominator can be smaller than the degrees of freedom for the numerator.

This makes option D false and hence the correct answer