The sampling distribution of the ratio of two sample variances $S _ { 1 } ^ { 2 }$ / $S _ { 2 } ^ { 2 }$ is said to be F-distributed provided that:
A) the samples are independent.
B) the populations are normal with equal variances.
C) the samples are dependent and their sizes are large.
D) the samples are independently drawn from two normal populations.

Question

Quizplus · Accepted Answer

The F-distribution is based on the ratio of sample variances from two independent samples drawn from normal populations, which is described in option D. Options A, B, and C do not accurately describe the conditions needed for an F-distribution.

The Sampling Distribution of the Ratio of Two Sample Variances S12S _ { 1 } ^ { 2 }S12​

The Sampling Distribution of the Ratio of Two Sample Variances $S _ { 1 } ^ { 2 }$