Forgive what may seem like a frivolous question, but I would very much hope to get a range of opinions on appropriate sampling strategy based upon what may seem to be a simple but perhaps interesting problem... I chose pasta as my example as I'm working with fibres at the moment and I'm feeling quite hungry!
Let's imagine that I decide to go home tonight and cook a big batch of spaghetti - for the sake of argument 500 individual strands.
That sounds rather uncomplicated, but, the trouble is, my wife sometimes chooses to tidy the cupboards and occasionally puts what's left of nearly empty packets of spaghetti in the pasta jar contaminating the spaghetti (all of the same type with a cooking time of 15 mins) that's currently in there - In other words, when I choose to make spaghetti, there may be a single population, or several sub-populations within the same jar - I just don't know and nor does she
This in of itself would be fine, but each type of spaghetti has a completely different cooking time (for the sake or argument one takes 12mins, one takes 15mins and one takes 18mins), each looks identical and overcooking or under-cooking results in horrid sloppy spaghetti or crunchy spaghetti respectively...
As the water comes to the boil I add my 500 strands of pasta and I wait for 15 minutes and test a single piece which is just perfect... al dente. I try another and its perfect.
The question is how many pieces of pasta would I need to taste before I can be confident (again the level of confidence is up to whoever chooses to reply - if they do) that the samples I have taken are representative of the bulk of pasta and that therefore I am unlikely to have any sloppy or crunchy surprises so to speak? Clearly the only way to be totally sure is to eat all 500 pieces, but given that I don't like pasta that much, perhaps not the most practical!
Without any prior knowledge (i.e. no idea how many contaminating strands of pasta have been added and of which variety i.e. 12/15/18 min) would I be right in assuming that without being very lucky in my testing, I would not be able to determine with confidence whether there are 1, 2 or 3 types of pasta present?