I want you guys to see here, two parts of the Z-test statistic were ultimately looked at; hence, the two blanks and yellow. The sign of the Z-test statistic was important, and the value was probably even more important. So, I'm going to skip a couple of pages when it comes to interpreting the Z-test statistic. I want you to see that it is important you both look at the sign of the Z-test statistic as well as the practical value of the Z-test statistic. So let's summarize what we just saw on this previous example. On this previous example, what we were doing was comparing the P_0 and the P-hat, and ultimately, in our previous example, we got a positive Z-test statistic. We got a positive Z-test statistic, and ultimately when you get a positive Z-test statistic, what that's emphasizing is the fact that P-hat is greater than P_0. When you have a positive Z-test statistic, it means your sample is greater than what is expected, meaning P_0. If your Z-test statistic ends up being a negative value like negative 3.5, where do you guys think P-hat is going to live in relation to P_0? Yeah, it's going to be less than. When Z is less than zero, your P-hat is going to be less than P_0. Literally, in terms of the location, when Z is positive, your P-hat is ultimately going to be to the right of the center, versus when Z is negative, P-hat will be to the left. So, that's one of the things that we can see when it comes to looking at the test statistic practically: the sign of the test statistic tells us the location of our P-hat. That's mildly important; it's good to know it, but really, the point of the test statistic is to help us identify how unusual our sample is. The point of the test statistic is to tell us how unusual our sample is, and ultimately what we saw on the previous example is that when your Z-test statistic is two or more away from the center, so when I say two or more, I mean our center is in the middle, you'll go one, two tick marks either to the right or to the left. And the idea is that if you have a Z-test statistic that is two or more standard errors away from the center, that is when we say we have an unusual sample. When Z is less than -2, is when we say we have an unusual sample. If Z is greater than two, that is when we say we have an unusual sample. And see, just like we saw in the last example, when your sample is unusual, we as jury members would be like, "That's weird, therefore that is evidence to discredit the null." That's what we just saw in our last example. And so we can then flip the switch: if your Z-test statistic is closer to zero, and when I say closer to zero, I mean your Z-test statistic is living somewhere between two standard deviations below to two standard deviations above the center, and that ultimately if your Z-test statistic is closer to zero, it means my data, my sample is not unusual, giving us not enough evidence. I would say between the two, really, this second half of the page is what is important. It's the value of the test statistic that will help me identify if my sample was considered unusual or not. I would say this page here is a really good page to put on your note sheet because this is a nice generalization page of what we're seeing with the test statistics.