Is there any way to calculate a confidence interval (or otherwise gauge the reliability of a sample) when you have a sample size of one and you don't know the population standard deviation?
I work at a farm. We sample our soil yearly for analysis and fertilize recommendations. For each relatively homogeneous field, the standard procedure is to take a number of samples, mix them together, and send a total of 1 lb of soil to the lab. If the field is 5 acres, that would be 1 lb of soil out of $\approx$ 10 millions.
The results would say that we have say 3 lbs of phosphorus per acre. Fertilizer recommendations would then be something like: For < 2 lbs phosphorus per acre, add 75 lbs of rock phosphate; for 2-4 lbs per acre, add 65 lbs; etc...
I've never been totally comfortable with this procedure, as I can't figure out how to put a confidence interval around the results. Is there a way to do so?