As N becomes larger, $\sigma _ { \bar { X } }$ becomes
A) smaller
B) larger
C) closer in value to the mean
D) farther in value from the mean.

Question

Quizplus · Accepted Answer

The standard error of the mean, denoted as $\sigma _ { \bar { X } }$, decreases as the sample size (N) increases. This is because the formula for the standard error of the mean is $\sigma/\sqrt{N}$, where $\sigma$ is the population standard deviation and $N$ is the sample size. As $N$ gets larger, the denominator of the fraction increases, making the overall value of $\sigma _ { \bar { X } }$ smaller.

As N Becomes Larger σXˉ\sigma _ { \bar { X } }σXˉ​

As N Becomes Larger $\sigma _ { \bar { X } }$