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?
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?

Updated On: Oct 1, 2024
  • Οƒ2n>Οƒ2n(Nβˆ’nNβˆ’1)\frac{\sigma^2}{n}\gt\frac{\sigma^2}{n}(\frac{N-n}{N-1})
  • Οƒ2n≀σ2n(Nβˆ’nNβˆ’1)\frac{\sigma^2}{n}\le\frac{\sigma^2}{n}(\frac{N-n}{N-1})
  • Οƒ2n<Οƒ2n(Nβˆ’nNβˆ’1)\frac{\sigma^2}{n}\lt\frac{\sigma^2}{n}(\frac{N-n}{N-1})
  • Οƒ2n=Οƒ2n(Nβˆ’nNβˆ’1)\frac{\sigma^2}{n}=\frac{\sigma^2}{n}(\frac{N-n}{N-1})
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The Correct Option is A

Solution and Explanation

The correct option is (A): Οƒ2n>Οƒ2n(Nβˆ’nNβˆ’1)\frac{\sigma^2}{n}\gt\frac{\sigma^2}{n}(\frac{N-n}{N-1})
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