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

The Correct Option is A

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