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 only applicable when the samples are independently drawn from two normal populations. Choice A is too broad and does not specify the normality assumption. Choice B specifies normality but also requires equal variances, which is too restrictive for F-distribution. Choice C refers to a paired sample design, which is not necessary for the F-distribution.

The Sampling Distribution of the Ratio of Two Sample Variances