Two independent samples are drawn from two normal populations,where the population variances are assumed to be equal.The sampling distribution of the ratio of the two sample variances is:
A)normal
B)Student-t
C)F
D)chi-squared

Question

Quizplus · Accepted Answer

The sampling distribution of the ratio of the two sample variances follows an F-distribution. This is because the ratio of two random variables that follow a chi-squared distribution divided by their degrees of freedom follows an F-distribution. In this case, the numerator follows a chi-squared distribution with degrees of freedom equal to the sample size minus one, and the denominator follows a chi-squared distribution with degrees of freedom equal to the sample size minus one multiplied by the pooled variance divided by the population variance. Since the population variances are assumed to be equal, the denominator follows a chi-squared distribution with degrees of freedom equal to twice the sample size minus two. Therefore, the ratio of the two sample variances follows an F-distribution with degrees of freedom equal to (sample size 1 - 1) and (sample size 2 - 1) for the numerator and denominator, respectively.

Two Independent Samples Are Drawn from Two Normal Populations,where the Population