Squeak is as usual correct. Statistics allow you to predict how accurate your outcome is by determining how likely it is that a sample would have the outcome you have if the underlying population did not have the criteria you hypothesize. But it will always be a likelihood.
If you flip a quarter 10 times and get 10 heads, statistics will tell you that the quarter is weighted and we will say that it is statistically significant at the 99% level. But we still don’t know it is true, because it will still happen with a normal quarter 1% of the time.
(z score=3.16 p hat is 1, and p is .5. Square root of .5*.5 is .5. Divided by square root of 10 is .158. Which means we are 3.16 stdevs off the mean.)
Stated differently, if you took 100 quarters and flipped each one of them 10 times, you could expect that one of the times you would have either 10 heads or 10 tails. If you do it with one quarter though, it is so unlikely that it will happen, that you can still conclude that it is weighted with reasonable certainty.
Torah613: Maybe what I just did is pretty basic, but I’m pretty proud of myself for knowing how to do it anyway and very few of my friends can do that.)