Question

R2.23: Which distribution listed below is formed by the distribution of sample variances: A. Chi-Square B....

R2.23: Which distribution listed below is formed by the distribution of sample variances:

A. Chi-Square

B. Student t

C. F

D. Exponential

Math   Statistics-And-Probability   
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Answer #1

Here Exponential distribution is not a sampling distribution. so we can remove the option.

Chi-Square distribution is formed by taking sum of squares of independent normal random variables. so it is wrong option

Students t is formed by ratio of independent normal and chi-square random variables. So this option is also wrong

F is formed by taking ratio of two independent chi- square random variables. we know the sample variance from normal distribution follows chi-square distribution. So we can say F is formed by taking ratio of sample variances. So the correct answer is option C, F-distribution

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