The spread of the sampling distribution of $\bar { X }$
Is ____________ the spread of the corresponding population distribution sampling distribution.
A)Larger than
B)Smaller than
C)The same as
D)Exactly ½

Question

Quizplus · Accepted Answer

The spread of the sampling distribution of $\bar{X}$ is smaller than the spread of the corresponding population distribution because the standard deviation of the sampling distribution of the mean is equal to $\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the standard deviation of the population and $n$ is the sample size. As $n$ increases, the standard deviation of the sampling distribution decreases. This means that the values in the sampling distribution are more clustered around the population mean, resulting in a smaller spread compared to the population distribution.

The Spread of the Sampling Distribution Of Xˉ\bar { X }Xˉ

The Spread of the Sampling Distribution Of $\bar { X }$