Hello Alastair,

Yes, there are methods for determining what size sample would be required in order to estimate some target parameter of a finite population with some desired degree of precision (at some target confidence level).

What impacts the resultant sample size required?

1. Method of sampling cases (Probability sampling method chosen).

2. Variability of the population (more variable = bigger sample).

3. Desired precision (more precision = bigger sample).

4. Target confidence level (higher confidence = less likelihood of missing the true value altogether = bigger sample).

5. Size of the finite population (vs. infinite population).

Here's a sample on-line calculator that helps estimate sample sizes under the assumption that simple random sampling will be the sampling method used (and that population proportion is the desired attribute): https://www.calculator.net/sample-size-calculator.html

If the goal is instead to assure that the proportion of acceptable units is at or above some threshold (e.g., 95%), then other methods, such as sequential sampling (or sequential probability ratio test) may be used.

Good luck with your work.

David Morse answered your question greatly. I must add that in practical applications like yours (usually unavailable enough of data due to budget), the specific opinions are of importance. The facility is a key factor to determine the size of the sample. Its weight can be calculated by the experts of the issue, better than a statistician. Albeit, as professor Morse said, the precision will be influenced.

Dear Alastair Howard ,

Just to add a little value to David Morse 's excellent answer: