I recently came in pocession of a fereign currency coin which seemed to be biased(to heads say). On noticing that the coin seemed asymmetric, I set up the experiment and started tossing the coin. Here is how things went :
after 2 coin tosses: 2H, 0T : Prob(H) =1
after 30 coin tosses: 15H, 15T : Prob(H) = .5
after 3000 coin tosses : 1492H, 1508T : Prob(H) = .497333333333333333333333333333
Now to state the obvious, the first result was a joke. In the third case, notice how I've conveniently written the number to more than 10 places of decimal. At some point, I had to stop and think, does it make any sense to claim the number to 10 places of decimal with just 3000 observations?
One thing I could agree upon was that, higher the number of observations, higher is the precision, but how much?
I guess I want to quantify precision as a function of number of observations.
Please share your thoughts on the problem, any suggestion would be appreciated.