Question

Which of the following CORRECTLY defines the relationship between the variances of sample means for simple random samples drawn with and without replacement from a normal population?

• A. $\frac{\sigma^2}{n}\gt\frac{\sigma^2}{n}(\frac{N-n}{N-1})$
• B. $\frac{\sigma^2}{n}\le\frac{\sigma^2}{n}(\frac{N-n}{N-1})$
• C. $\frac{\sigma^2}{n}\lt\frac{\sigma^2}{n}(\frac{N-n}{N-1})$
• D. $\frac{\sigma^2}{n}=\frac{\sigma^2}{n}(\frac{N-n}{N-1})$

Answer 1

Answer: (A)

$\frac{\sigma^2}{n}\gt\frac{\sigma^2}{n}(\frac{N-n}{N-1})$

Answer 2

The correct option is (A): $\frac{\sigma^2}{n}\gt\frac{\sigma^2}{n}(\frac{N-n}{N-1})$