Can a small sample size with applied machine learning provide higher accuracy than the sample size alone?

Question

Say I have 4000 apples and I want to know the percentage of apples that are red and the percentage that are green. Using only a sample, I could randomly pick and classify ~351 apples to report with a 95% confidence level and a 5% confidence interval what the percentage is.

My question is, if I build a highly accurate machine learning model on a sample size of ~100 apples (let's say it's over 99% accurate), then apply it to the remaining ~3900, could that give me a better estimation of the total population of 4000 apples?

Answer 1

If I am understanding your question, you are wanting to compare the accurate machine learning model with ~100 samples to the ~351 samples on a 95% confidence interval.

If that is the case, then I believe it is correct to say that the accurate machine learning model would give a much better estimation of the total population. By looking at the Central Limit Theorem (measure of sample means approach a normal distribution as samples increase; we want >30), we can see the ~100 samples definitely meet the criteria. Even though you have fewer samples, the accuracy helps. As you increase the samples, it will get more accurate obviously, but not very dramatically.