Suppose that many large samples are taken from a population whose data values have a standard deviation of 512.34. Which of the following could be the standard deviation of the sample means?

A) 34.16
B) 1534.16
C) 2034.16
D) 1034.16

Question

Suppose that many large samples are taken from a population whose data values have a standard deviation of 512.34. Which of the following could be the standard deviation of the sample means?

A) 34.16
B) 1534.16
C) 2034.16
D) 1034.16

Vocaloid · Answer

by definition the standard deviation of the sample means = population standard deviation / sqrt(sample size)

so by definition the sample mean standard deviation must be smaller than the pop standard deviation