Q.A quality-control department finds that the population standard deviation of the fill-weight of a certain packaged product is 20 gm. If a random sample of 100 packets is drawn, find the standard error of the sample mean.

Sampling error is the difference between a sample statistic and the true population parameter that arises purely because a sample, not the whole population, was studied — it falls as sample size rises and vanishes in a census. Non-sampling error (questionnaire flaws, non-response, interviewer bias, recording mistakes) can occur even in a census and does not necessarily fall with sample size.

The standard error of the sample mean quantifies sampling error precisely:

Because $n$ is under a square root, the sample size must be quadrupled to halve the standard error — SE falls only as $\sqrt{n}$, not as $n$ itself.