The sampling distribution of the ratio of two sample variances 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
E) none of these

Question

The sampling distribution of the ratio of two sample variances  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 
E) none of these

Quizplus · Accepted Answer

The F distribution is the ratio of two sample variances and is applicable when the samples are independently drawn from two normal populations. Choice A is not sufficient on its own to ensure that the F distribution is applicable, as the independence of the samples does not guarantee that the populations from which they are drawn are normal. Choice B is incorrect because the populations are not necessarily required to have equal variances for the F distribution to be applicable. Choice C is also incorrect as the F distribution assumes independent samples, not dependent ones.

The Sampling Distribution of the Ratio of Two Sample Variances