A random sample of size 50 is taken from a large population with mean μ=160 and standard deviation σ=18.

Question

A random sample of size 50 is taken from a large population with mean μ=160 and standard deviation σ=18. What is the mean of the sampling distribution of the sample means? What is the standard error of the sampling distribution of the sample means?

Answer 1

The mean of the samples is expected to be close to that of the population.

The standard error of the sample means is the standard deviation of the population divided by the square root of the number of items forming the sample mean, here sqrt(50), thus approximately the standard deviation divided by 7.07.