All right, guys, step one is done. Step one is done. Where what we wanted to do was prove we had a good sample. Step two is then where we do the fun stuff. Step two is then ultimately the calculator work. So let's go back to the previous page and identify what are the steps we need to take on our graph and calculator, and we're going to focus on the orange step. I want you guys to look for the "Stat" button. And if you're like, "Wait, Stat button, third row down, third column over, I know that button. That was where we entered in all our data back in Chapter 2 and 3." I know the "Stat" button because if I toggled once to the right, that's where "Calc" was. That's where I did one 1-VarStat. I used that to find mean and median. Well, guys, we're going to toggle over one more time to the "Test" column. As I mentioned at the beginning of the semester, you're going to hit that "Stat" button so much this semester, and this is now the first time we're going to end up in the test column. Now I'm going to let you guys know, we're pretty much going to live off different test functions for the rest of the semester. I'm literally going to teach you eight to nine tests. Yeah, eight to nine tests by the end of the semester. And so with that in mind, get comfortable doing these two steps: go to "Stat", go to "Test", and the one you guys want to find is "1-PropZInt." It's going to be Row A. So notice it starts with row one and then two, three, four, five, six, seven, eight, nine, zero, and then 'A' pops up. So I want you to go to 1-PropZInt. And what I want you to know is that in 1-PropZInt, you have a total of three values you need to plug in. The first value you need to plug in is 'X,' the number successive. The second value is 'n,' sample size. And the third value is confidence level. And the beautiful thing, guys, is that all three of these numbers are going to directly come from your prompt, from the black portion of your notes. All right, so let's do that. Let's do this together, guys. 'X.' 'X' is going to represent your number of successes. Can you guys tell me, based on what we saw above, what is the number of successes? Yeah, notice it's that number of successes that we gathered in Step One to prove if we had enough successes. So, guys, literally you're going to take that number you utilized in Step One, and you're going to use that as your first input: 518 for 'X.' Your second input is sample size, and sample size will be a number explicitly given to us in the prompt. What is our sample size here? Yeah, the sample size is that 1,154 people. Notice we use that number when calculating the number of failures: 1,154 people. Let's type that in. Lastly, confidence level. The confidence level is going to be that percentage of a confidence interval we wanted to form. So you look for the word "confidence interval," and then you look for the percentage in front of that: 95%. And in particular when you type it into your calculator, you're going to write that as a decimal, .95. That's all you got to do, guys. Just find the numbers from the prompt. And that's why I told you this is going to be so much easier than doing any of the calculations, because all you do after this is now hit enter. And bam! Confidence interval given to you. Some calculators are going to give your answer with a lower and upper row of responses. Some calculators are going to write it as parentheses with a comma, and again the same two numbers, .42 and .48, written in between those two numbers. In either result, regardless of how your calculator presents it, I want you guys to see how easy this was. It was push a couple buttons to get to 1-PropZInt, type in three numbers, hit enter, and it gave us my confidence interval. Because from there, then we go to step three: interpret it into a practical question. And the great thing about this interpretation is that this is totally a template you can use over and over and over again. And the beautiful thing about this template is you have already identified each one of these ideas somewhere in the rows above. And this is why I like to color-code my notes, because this is really going to make it pop out. Now see, in the template, you need to list how confident you were. Well, we already acknowledged that. We already said we're 95% confident in step two. Yeah, use that number. We are 95% confident that between these two percentages, and you're literally just going to take the lower and upper values of this confidence interval and convert that from decimals to percentages. And remember, you do that by simply multiplying each of those decimals by 100%. So we are 95% confident that between 42% and 48%, we are 95% confident that between 42% and 48% of all—and so of all emphasizes then we need to go back up to the previous row and identify what was my population—it was adult Americans—so let's keep the sentence going. We are 95% confident that between 42% and 48% of all adult Americans are what? Well, then it's my characteristic of success, my characteristic of success from earlier, which was willing—willing to pay higher prices to protect the environment. I want you guys to see we're literally copying and pasting pretty much everything we learned in one of the two steps above. And so honestly don't memorize this template, put it on your notes sheet, and then know how to interpret every confidence interval using this template. Here's the thing: confidence intervals are fantastic, confidence intervals give so much information, but confidence intervals are usually not the end game. Confidence intervals are merely a tool to answer practical questions. For instance, let's say you are an environmentalist and you are trying to pass a bill. You are trying to pass a bill that will increase prices so that it will lead to practices that will protect the environment. You, the environmentalists, are trying to pass a bill so that this bill will raise prices to protect the environment. Now you need to bring it to Senate. You need to bring it to Senate and Senate says, "Well, here's the thing: for your bill to pass, you need to prove 50% of Americans are on board. You need to prove that 50% of Americans are in fact willing to pay more to protect the environment." And so you, the good environmentalist who has some statistical background, goes out, goes out and grabs a random sample of 1,154 people, and you find 518 are willing to pay more to protect the environment. This gets you really excited. You do all of the conditions checking, you do the calculation of the confidence interval, and in your research you then find this interpretation: "I'm 95 % confident that between 42% and 48% of all Americans are willing to pay higher prices to protect the environment." But what's the issue here? The issue—the issue is Senate says you need 50. You need 50% of Americans to be on board. 50. And my question for you is that if we're looking at this confidence interval, if we're looking at this confidence interval 42% to 48%, if we're looking at this confidence interval of 42% to 48% which are representing possible percentages of all Americans who are willing, meaning any percentage in this orange box represents the possible percentage of Americans who are willing, it could be 42%, 43%, 47%, my question for you is 50%, is that in my confidence interval? No. And what is the issue with that? What is the issue with the fact that 50%, my restriction, is not in the interval? It's then emphasizing that our research showed that what we need does not exist, since the entire confidence interval does not include this restriction, does not include this restriction of 50%. What this is emphasizing is then that 50% of adult Americans are not—not willing. You're not willing to pay higher prices because anything outside of the orange confidence interval is then implausible percentages, meaning instead of our—it's not really so. As the environmentalist, you'd be bummed, but at least you were able to show that the Senate won't approve it without having gone through the whole process. This was the first real example we did with confidence intervals where what I want you to see in Part B is this is really the application of confidence intervals. This is the application of a confidence interval. And so when it comes to working with confidence intervals, there will always be these three steps: check the conditions for a good sample, use your calculator to find the confidence interval, and interpret the confidence interval in a template. But at the end of the day, it's not enough to just stop at the interpretation. We want to figure out how can I use it in the real world, what are applications of the confidence intervals. And so in a lot of ways, the application, the bonus step of when using and creating a confidence interval, I'm going to let you guys know right now, you are going to see something like this on your exam. You are going to see questions that are going to ask you each of these three steps, ask you applications of the confidence interval. And the reason for that is I want to know you know the three steps of the confidence interval. I want to know you know how to apply the confidence interval.