The Cola Nut experiment

Hypothesis tests can be about anything.

Sometimes they're about cola nuts. Suppose I told you that exactly one piece of cola nut in this bag is poisoned, and that there are 20 pieces in the bag. Would you be too worried about getting poisoned?
What if there were only 10 pieces?
What if there were 100 pieces?
In all of these cases, you should be too worried. But you realize that it could happen just by chance. So we can always get an extreme value "just by chance".
Those are our usual alpha levels: 0.05, 0.10, 0.01.
When we do hypothesis tests, we look for extreme values, which we suspect indicate that "the setup" was not as stated. That, perhaps in this case, more than one piece of cola nut is poisoned.
If you took a piece of cola from the bag and died, would you chalk it up to bad luck? Or might you suspect that I've poisoned more than one out of 20! (Did you see the Princess Bride?)
A man enjoying his cola nuts....

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