Solution
Halving the Standard Error
Show the problem again
Your estimate of a population mean from a random sample of size n has standard error SE. How large a sample do you need to cut the standard error in half?
Worked solution
The answer is 4n. The standard error of the mean is σ/√n, shrinking with the square root of the sample size. Halving it requires √n to double, i.e., quadrupling n. This square-root law is why precision gets expensive: each additional digit of accuracy costs a 100-fold increase in data.
Source: Standard standard-error exercise from introductory statistics texts. Statement written for AxiomIQ.