As the size of the random sample gets larger, what happens to the standard deviation of the distribution for the sample mean?
A) It gets larger.
B) It gets smaller.
C) It becomes normal.
D) It goes to 1.

Question

Quizplus · Accepted Answer

As the sample size gets larger, the standard deviation of the distribution for the sample mean gets smaller. This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, as the sample size increases, the variability of the sample mean decreases, resulting in a smaller standard deviation.

As the Size of the Random Sample Gets Larger, What