Track 6 · Sampling and the Central Limit Theorem · Lesson 8 of 8
Sample size, precision and cost
Plan the sample size needed for a target margin of error, explain the diminishing returns of larger samples, and allow for nonresponse.
A survey team quotes 400 interviews for a ±5-point margin of error. The client asks for ±2.5 points “for a bit more money” — and is told it will cost four times as much. Precision grows only with the square root of the sample size, and every planning decision follows from that fact.
Because , precision improves with the square root of the sample size. Doubling cuts the SE by only ; halving the SE needs four times the sample; cutting it to a tenth needs a hundred times. Costs, meanwhile, usually grow in proportion to . The first few hundred observations buy a lot of precision; each extra thousand buys less.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Plan the sample size for a target margin of error for a mean or a proportion, rounding up
- Explain why halving the margin of error needs four times the sample
- Inflate a planned sample for the expected response rate
- Weigh extra precision against cost, and separate precision from bias