One more, another head.

Another head, and lastly yet another head. So in this case, our

sample proportion, or the proportion of success, is seven over eight or 0.875.

We record this

number, and we're going to collect these on the

dot plot, dot plot at the bottom of the screen.

For the second simulation, we once again have eight slots, and

we toss the coin eight times and we record the outcomes.

And in this case we have three out of five heads.

So our proportion of success here would be 0.375, and

we record that number on our dot plot as well.

Another simulation,

yet another set of eight flips, and then we

will want to count how many of those were heads.

So that seems like five out of eight, and we want to record that number as well.

We can keep doing this forever, and we would want to do it as many

times as possible, but for illustrative purposes, we're

only going to really get to ten simulations.

So let's say that at each iteration we're

collecting these data the simulated p hat, and finally

when we get to the last simulation again we roll the coin eight more times.

Seems like we have six out of eight heads, for 0.75.

So this is what our simulated distribution looks like for p hat.

Obviously, if in fact we actually had done a lot of simulations, as

we should, the shape of the simulation would look maybe only slightly different.

We would definitely have more

observations, and the shape should probably follow something similar to this,

but ten simulations is definitely not sufficient to make a call.

However, based on this and based on the definition of

the p-value, as the probably of observed or more extreme outcome.

So in this case, our observed outcome was 100% success.

So the p-value can be defined as what is the probability of

100% or more success, which doesn't even exactly make sense,

given that the true rate of success was only 50%.

We don't have any data, any simulated sample proportions that

actually fit the bill, so based on this simulation, our p-value is zero.

It's probably usually a good idea to say that it's almost zero.

And chances are if we had actually done

this properly with about 10,000 or so simulations

we would get a number that's small, which

would probably also yield a rejection of the

null hypothesis, but it may not be exactly zero.