Correct option is A
The correct answer is (a).
Introduction
The F-distribution is a continuous probability distribution heavily utilized in statistical hypothesis testing, specifically in ANOVA.
The variance of an F-distribution depends strictly on its two degrees of freedom.
By plugging the given parameters into the standard mathematical formula for F-distribution variance, we can compute the precise statistical dispersion.
- The parameters for an F-distribution are its degrees of freedom, denoted as (numerator) and (denominator).
- In this problem, the parameters are given as
- The variance of an F-distribution is valid only when
- The formula for the variance is:
-
- Calculating the numerator:
- Calculating the denominator:.
- Dividing the values yields , which rounds to 1.587.
- Option B (1.378): This is an incorrect mathematical calculation and does not result from the standard variance formula of the F-distribution for the given parameters.
- Option C (2.578): This value is substantially higher than the actual variance and implies a misapplication of the degrees of freedom in the formula.
- Option D (1.498): This is a numerically close distractor but mathematically incorrect for degrees of freedom 5 and 9.