
So this is where we draw the line, any outcome over here is critical.

That means so any of those outcomes, you'll be so surprised that we reject the null hypothesis.

Whereas any outcome in the region over here is okay, so we accept it.

Notice subtlety here. Even outcome 11 is okay.

Despite the fact that 11 is very surprising, it comes to the probability less than 5%,

but that's not the way to look at this.

The more frequently your sample, the more unlikely each individual outcome is.

Look at the outcome as blocks.

When you implement hypothesis testing, there'll be something like a most likely outcome.

Somewhere between 13 and 14, I guess it's 14. That outcome has to be okay obviously.

If you see that, you'll be happy and then you push this in one direction towards H₁,

the alternate hypothesis until all the probabilities remaining

cover 5% or less and that's the critical region.

So let's give this another try. Last Saturday, I went to the magic store and bought a loaded coin.

I paid a lot of money for it and the wizard that sold me the coin told me

the probability of head is equals 0.3.

In fact, there are many buckets of coins, the fair ones

the slightly loaded, all the way to the fully loaded, and those guys are cheap and those guys are cheap

but this one over here was really expensive.

So I wanted to make sure that I really got a loaded coin.

Let's first ask, what's our null hypothesis. Here are our choices for the probability of heads.

Pick the one that's best describes the null hypothesis.