Question

Consider an x distribution with standard deviation σ = 18.

(a) If specifications for a research project require the standard error of the corresponding xbar distribution to be 3, how large does the sample size need to be?
n = ________

(b) If specifications for a research project require the standard error of the corresponding xbar distribution to be 1, how large does the sample size need to be?
n = _________

Answer 1

Let X be a random variable with standard deviation

a) Let be the sample mean of a randomly selected sample of size n.

We know that the standard error of mean (or standard deviation of ) for a sample of size n is

We need the standard error to be 3. Hence the n is

ans: n=36

b) We need the standard error of mean to be 1

ans:n=324