Consider a random sample with sample mean $\overline{x}$. If the sample size is increased from n = 40 to n = 360, then the standard deviation of $\overline{x}$ will
A) remain the same.
B) increase by a factor of 9 (will be multiplied by 9).
C) decrease by a factor of 9 (will be multiplied by 1/9).
D) decrease by a factor of 3 (will be multiplied by 1/3).

Question

Quizplus · Accepted Answer

The standard deviation of the sample mean, often denoted as $\sigma_{\overline{x}}$, decreases with the square root of the sample size (n). Therefore, increasing the sample size from 40 to 360 (which is a factor of 9) decreases the standard deviation of the sample mean by a factor of the square root of 9, which is 3. Hence, the standard deviation of $\overline{x}$ will decrease by a factor of 3.

Consider a Random Sample with Sample Mean x‾\overline{x}x If the Sample Size Is Increased from N =

Consider a Random Sample with Sample Mean $\overline{x}$ If the Sample Size Is Increased from N =