Which of the following statements is true about the standard deviation of $\overline{x}$ ?
A) It decreases as the sample size n increases.
B) It increases as the sample size n increases.
C) It does not change as the sample size n increases.
D) It changes each time a new sample is drawn.

Question

Quizplus · Accepted Answer

The standard deviation of the sample mean ($\overline{x}$) decreases as the sample size (n) increases. This is because the standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size ($\sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$), indicating that as n increases, $\sigma_{\overline{x}}$ decreases.

Which of the Following Statements Is True About the Standard x‾\overline{x}x

Which of the Following Statements Is True About the Standard $\overline{x}$