Since all three conditions hold (random sample, large sample, large population), we then can go to step three and type everything into our calculator. That ultimately the steps we're going to take to use our calculator is we're going to go to "Stat", toggle to the third option of "Test", and we're going to use 1-PropZTest, so option number five. And again, when you type that into your calculator, I want you to note that in 1-PropZTest, you're going to need to find the value of P_0, the value of X, the value of N, and then the last row, the correct inequality to use. But here's the cool thing: all four of these colors I just drew on the board, all of these colors we just drew on the board, are literally what we have already identified in the previous rows above. P_0 we already know, we already identified, that we already identified P_0 is 0.90. The X, the number of successes from this sample, are only used in step three. We only use X in step three. So, in my calculator, when you see that row that says X, X is going to be that number of successes from my sample. So in this case, that 160 that you're going to plug in for X, you pick 160. I want you to know we're not picking the 167 from step two earlier. No, no, no, we're picking the 160 because X and N are both representing values from my sample. In this case, particularly, X is the number of successes from the sample from the prompt. And then from there, N, we already said N was 185. So let's type that in. P_0 will be 0.90. X will be 160. N will be 185. And so the big question then is which inequality will I use? Yeah, not equal. You literally take the inequality from your alternative hypothesis. So in this case, P does not equal P_0. So typing all of that in, picking the not equal to, we can hit calculate and we see we'll get a Z test statistic of 1.59 and a P-value of 0.11. When it gets then to step four, when it gets to the decision step, the decision step is going to require you to go back to step three and identify the P-value of 0.11 and then go back to step two and identify the significance level, the significance level of 0.10. And again, the point of the decision step is you need to identify the relationship between P and the significance level and really ask the question, is P bigger or smaller than the significance level? So why don't you guys give me a hand with that 0.11? Is it bigger or smaller than 0.10? Yeah, in this case, we see here my P-value is bigger. I can see here my P-value is bigger. When P is bigger, that means we fail to reject the null. Why? Well, let's go back and remember what P-value represented. Remember, P-value is ultimately representing how surprised I feel. And going back a couple of pages, remember that the bigger the P-value, the less surprise you will be because the bigger the P-value is, the closer your sample is to the center. And so what that means is your sample seems pretty ordinary. And as we know from watching crime shows, when you hear a testimony, when you hear a report that seems totally normal, you won't be surprised. Therefore, that's not enough evidence. We fail to reject the null. So what we're seeing is our first relationship here that when your P-value is bigger, we will fail to reject the null. And there's no significant evidence. These three things I'm writing in red, when P is bigger, you fail to reject the null. And that ultimately, there is not enough evidence. These three ideas are always going to go together when it comes to hypothesis testing. It's like the famous trios like Ron, Harry, and Hermione, where ultimately, when your P-value is bigger, it will start the same domino effect of saying when P is bigger, you fail to reject the null, and therefore, there's not enough evidence. These three will always go together until the end of time, to the end of this semester, to the end of chapter eight, to the end of chapter nine, for every single exam. These three will always go together, ultimately emphasizing there is not enough evidence. And not enough evidence of what? Well, ultimately, not enough evidence showing the question I wanted to answer, is the proportion of Chinese restaurants which fail after one year different than 90%? Well, there's not enough evidence showing that difference. That is what ultimately the conclusion is emphasizing. We're ultimately going to answer the question: in this case, there is not enough evidence showing that the proportion is different, that the proportion is different for Chinese versus all restaurants. So honestly, how do you end the conclusion statement in green? Regurgitate the question. Literally, for all the English people in the room, rewrite the question into a sentence. That's all we're doing with that last step.