Consider a sampling distribution formed based on n = 9.If the standard deviation of the population of individual measurements is $\sigma$
,then the standard deviation of the population of all sample means $\sigma _ { \bar { x } }$
Equals ____.
A) $\frac { 1 } { 3 } \sigma$
B) $\frac { 1 } { 9 } \sigma$
C) $3 \sigma$
D) $9 \sigma$
E) $\frac { 1 } { 81 } \sigma$

Question

Quizplus · Accepted Answer

The standard deviation of the sampling distribution of the sample mean, $\sigma_{\bar{x}}$, is equal to the population standard deviation, $\sigma$, divided by the square root of the sample size, $n$. Given $n = 9$, $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{9}} = \frac{\sigma}{3}$, making option A correct.

Consider a Sampling Distribution Formed Based on N = 9 σ\sigmaσ

Consider a Sampling Distribution Formed Based on N = 9 $\sigma$