I was discussing a small experiment with a friend of mine this week. He said, "we can just do 3 trials."
I said, "sure, but the subject will have to get all 3 trials right to be better than chance."
We discussed it a bit and verified that you would indeed have a 50/50 chance of correctly guessing at least 2 out of 3 coin flips.
I started wondering how many trials you'd have to have to get statistical significance. I figured out that the probability of guessing at least $n-1$ correct trials is this formula:
$\frac{(n + 1)}{ 2^n}$
If I set that equal to $.05$, how do I out how many trials you'd have to have to get a 95% confidence if the subject misses no more than one trial?
id est, if $.05 = \frac{(n + 1)}{ 2^n}\,,$ what is $n$?
More importantly, how did you solve for $n$?
Thanks a lot!
Patrick