[mrmr]

Okay, okay, let's see what we can do here.

The full cheesy story: You store the baseballs in crates along with various other sports collectables, sorted by year. You replaced your windows with plexiglass in 2001, so you don't bother looking through the 2002+ crates. You gather all the baseballs (it turns out there are 2000) then devise and employ some clever technique to randomly select 100 of them.

You collect your data, and then retire to your office to estimate and calculate, when it hits you (like a bad pitch through a livingroom window), that it was 2003, not 2001, when you installed the plexiglass. You go back and pull out your 2002 and 2003 crates, and count 650 baseballs.

You begin to wonder, must I take some seperate sample out of the 650 to get a reasonable estimate, and to determine how accurate and precise said estmate is? Or throw out my data and start over with a new random sample out of 2650?

Before you can think the problem through, much less begin some re-sampling process, the ghost of Babe Ruth appears before you and says: "I'm hungry for baseballs," and eats all of the baseballs. Before disappearing, the ghost of the Babe tells you, in one long sustained belch, "I have some hidden wisdom for you from beyond the grave: there is no reason to think that the 2002 and 2003 baseballs are any different from the older ones, and before some stickler gets clever on us, let me add that the baseballs, the windows, and the neighbor kids, Ceteris and Paribus, all remained relatively unchanged over the years, and had no serial correlations to speak of."

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I don't know how or why I thought of this problem, but I asked it here because after reading "Sampling," by S. Thompson, I still couldn't answer the question in a mathematically (or logically, if it doesn't come to math) rigorous way. I think I could figure it out if I keep working on it, but why would I do that, when I've got 2+2 to answer it for me?!

Actually, it seemed like a good logical puzzle, so I thought I'd share it.

Still interested in an answer, and more importantly, a line of reasoning that supports it.

Edit: posted before madnak's reply. I welcome more input, though.