Question

The standard error of a distribution of sample means is __________ than the standard deviation of a population of individuals it came from because most of the sample means will be __________ to the mean of the population of individuals

Answer 1

If the population standard variance is s and we have a sample of size n from that distribution then it can be shown that standard error of the sample mean will be equal to s/√n.

As n is more than 1 hence s/√n is less than s.

Thus the standard error of sample mean is always less than the standard deviation of the population of individuals.

This is because the as we sample more and more values, the sample mean becomes more closer to actual population mean and gets more concentrated around it. Hence the standard error becomes much less.

So the correct answer is:

The standard error of a distribution of sample means is __less___ than the standard deviation of a population of individuals it came from because most of the sample means will be _____equal(or close)_____ to the mean of the population of individuals.

Hope the solution helps. Thank you.

(Please comment if further help is required)