The sampling distribution of a mean with a sample size of 50…
A) has a smaller standard deviation than a sampling distribution with the same mean of sample size 30.
B) has a smaller standard deviation than a sampling distribution with the same mean of sample size 60.
C) has the same standard deviation with the distribution of individual raw data in the population.
D) has a different standard deviation than a sampling distribution with the same mean of sample size 100 but we do not know whether the standard deviation will be larger or smaller unless we know the standard error.

Question

Quizplus · Accepted Answer

The standard deviation of the sampling distribution of the mean decreases as the sample size increases, assuming the population standard deviation is known or the sample size is sufficiently large to estimate the standard deviation using the sample. Therefore, a sample size of 50 will have a smaller standard deviation than a sampling distribution with the same mean of sample size 30.

The Sampling Distribution of a Mean with a Sample Size