3. Consider the following statements about the F distribution: (i). One characteristic of the F distribution...

3. Consider the following statements about the F distribution:

(i). One characteristic of the F distribution is that F statistics cannot be negative.

(ii). There is one unique F distribution for a F-statistic with 29 degrees of freedom in the numerator and 28 degrees of freedom in the denominator.

(iii). The F distribution’s curve is symmetric around its peak when the degrees of freedom for the numerator and for the denominator are equal.

Which of the following is true?

Expert Solution

i. F distribution is never negative it is always greater than or equal to 0. It is a probability density function used especially in analysis of variance and is a function of ratio of two independent random variables ,so it is always non negative. So it is TRUE.

ii. TRUE. There is unique F distribution for 29 degree of freedom for numerator and 28 degree of freedom for denominator. F distribution is unique for all different sets of variance. It changes with change in degrees of freedom of numerator and denominator.

iii. FALSE. F distribution is not symmetrical and is always right skewed. It becomes more symmetrical with increase in degrees if freedom , it becomes more like normal distribution. But it is not symmetrical in any case.

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orchestra answered 1 year ago

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