A sample can represent a population. Accuracy and precision is dependent upon the statistical method used.
Economic transactions are not fish in a lake. You can't cast your net and collect a bunch of them at random.
You get the ones you go looking for, which is not how you collect a sample. The only way out is to get them all, which is not possible.
So the entire statistics profession is wasting its time? This is indeed news.
If a statistician pulled marbles from an urn while looking and deliberately choosing the ones he wanted, wouldn't you be even a little suspect when he started making claims based on the notion that his sample was random?
You are attempting to refute Hayek's central point from
The Fatal Conceit, namely that preferences aren't knowable except through the proper functioning of the market. Better than you have tried and failed, though they usually have the decency to sit through a freshman statistics course first.