Our decisions about this test can be that we do not reject the null hypothesis or that we reject it. We either reject the null hypothesis or we don't, according to the test. Now, the two possibilities for the truth of the situation is this. If the null hypothesis is either true or it's false. That is if the mean is equal to some value or that it's less than, greater than or not equal to. So the null hypothesis is true or it's false. Now, if the null hypothesis is true and we do not reject the null hypothesis, then we've made a correct decision. Now let's go to the graph and talk about that. This is true and the X bar lands in this region, so we do not reject. All right, that's a correct decision. This was true, we landed in this do not reject region. Great. Now, what if the null hypothesis is true and we reject? That is, in our sample we have one of those strange samples where we lie outside of a reasonable error or a reasonable area, then that's a type one error and it's probability is alpha. Let's go over here and talk about what that is. We talked about it before. This is true and yet we have a strange sample where X bar landed in the rejection region and we reject the null hypothesis. Now that's a type one error and it's probability is alpha. OK, the other situation. The null hypothesis is false. In our problem it is not the case that the average mileage for this automobile is 47 miles per gallon. It is not the case. Now, and we do not reject HO. Wow, this average mileage is not 47 miles per gallon, let's say it's less than 47 miles per gallon and yet we land, X bar lands in this region, we do not reject, that's a beta error. That's a type two error and it's probability is beta. Now the last situation is that the null hypothesis is false and we reject it. That is we caught on to the situation. The null hypothesis is less than 47 miles per gallon in this problem and we reject that null hypothesis and accept the idea that the average mileage is less than 47 miles per gallon. That's a correct decision.