The sampling distribution of the ratio of two sample variances is said to be F-distributed provided that:
A) the samples are independent from any distributions.
B) the populations are normal with equal variances.
C) the samples are matched and their sizes are large.
D) the samples are independently drawn from two normal populations.

Question

The sampling distribution of the ratio of two sample variances  is said to be F-distributed provided that:
A) the samples are independent from any distributions. 
B) the populations are normal with equal variances. 
C) the samples are matched and their sizes are large. 
D) the samples are independently drawn from two normal populations.

Quizplus · Accepted Answer

The F-distribution is defined as the ratio of two independent chi-squared distributions, each divided by their respective degrees of freedom. Therefore, the condition for the sampling distribution of the ratio of two sample variances to be F-distributed is that the samples are independently drawn from two normal populations.

The Sampling Distribution of the Ratio of Two Sample Variances