Do cows fly?

A friend tells us that cows fly. We decide to settle it with a p-value, so first the claim has to say how much they fly: a cow that flew for no time at all would be no different from a cow that does not fly. Our friend says every cow spends some hours a day in the air, and the farm we are going to has a certain number of cows.

If that is true, then at the moment we look over the gate each cow is airborne with probability hours / 24, and the number of cows we should catch in the air follows a binomial distribution.

We go to a farm, we look, and every cow is on the ground — which is what every visit to every farm finds. So what changes from one experiment to the next is not the result but the farm: each one is picked at random, up to the size set below, and the same empty sky means something very different over a herd of nine and a herd of ninety. So the plot is over the farms themselves: one bar for every farm we might walk into, and its height is the p-value of finding every cow in it on the ground. The cutoff is the line across them, and the red bars are the farms big enough to reject the claim.