Asked by Elise Weidman on May 25, 2024
Verified
Which of the following statements is correct regarding the percentile points of the F distribution?
A) F0.10,10,20 = 1/F0.90,10,20
B) F0.90,10,20 = 1/F0.10,20,10
C) F0.90,10,20 = 1/F0.90,20,10
D) F0.10,10,20 = 1/F0.10,20,10
Percentile Points
Points or values below which a certain percentage of observations in a dataset fall, used to measure the relative standing of a value within a dataset.
F Distribution
A probability distribution that arises in the analysis of variance and is used in hypothesis testing and confidence interval estimation for two sample variances.
- Gain an understanding of the properties and parameters related to Student t, chi-squared, and F distributions.
Verified Answer
AS
Ahmad SahyounMay 27, 2024
Final Answer :
B
Explanation :
The correct statement regarding the percentile points of the F distribution is that the F value at a certain percentile for a given numerator and denominator degrees of freedom is the reciprocal of the F value at the complementary percentile when the degrees of freedom are reversed. This is accurately represented in option B, where F0.90,10,20=1F0.10,20,10F_{0.90,10,20} = \frac{1}{F_{0.10,20,10}}F0.90,10,20=F0.10,20,101 . This property is a result of the relationship between the F-distribution and its inverse under the swapping of degrees of freedom and complementing the percentile level.
Learning Objectives
- Gain an understanding of the properties and parameters related to Student t, chi-squared, and F distributions.