What I want us to do with wrapping up Section 7.2 is just practically use these two formulas I boxed in green and blue above. In Example Three: Only 65% of insured women get annual Pap tests. Find the mean and standard deviation of the sampling distribution of the sample proportion of women who get annual Pap tests with a sample size. Okay, what I want to do is I want to find the mean and I want to find the standard error. So, find the mean. Find the mean of the sampling distribution. When we say find the mean, it's really answering the question in Part A: What value do we expect for our sample proportion when we are asked the question? What value should we expect? The word "expect" is emphasizing the idea of "typical". What should typically happen? When you see the word "expect", it means you want to figure out, well, what typically should be the case? And remember, in Chapter Three, we learned the word "typical" means "mean". I want to find the mean of all my sample proportions, sample proportions p-hat, and that formula above then ultimately says that the mean of all my sample proportions should equal my population proportion P. Should equal my population proportion P, and in this particular problem, we were lucky enough to be given. In this problem, we were lucky enough to be given P = 0.65. We were lucky enough to be given the population proportion. So, in this case, this first question, find the mean of the sampling distribution, well, the mean of the sampling distribution will then just be the population proportion: 0.65. Standard error. Standard error is then going to be that standard error formula that I gave you guys above. If you're being asked to find standard error, you're using the formula for standard error. In standard error, I want you guys to note P, the population proportion is listed in there. So that already means when it comes to filling in this square root formula, we're going to write 0.65 both before the parentheses as well as inside the parentheses. What is n? Yeah, let's remember, sample size is going to be that value of n. So in this case, when you see the letter n, keep in mind that is the sample size. And then from there, it's about practically plugging this into your graphing calculator and making sure we know how to get that final number. So when it comes to evaluating the square root, first thing you gotta do is you need to write the square root symbol, all right? How do you get to the square root symbol? You do "2nd" and the "x^2" button, and what you should see pop up on your calculator is a square root expression. Now, some calculators are going to need you to then draw a parentheses. Draw a parentheses to say everything else that's about to follow is inside the square root. So you'll need to draw parentheses first. Parentheses, this is going to be the first parenthesis we just drew. And then from there, you type in across the top, then the division, and then on the bottom. So we'll write that [0.65×(1−0.65)]. Close the parentheses. So what I just did is I wrote clear across the top, then you need to do the division symbol and then type in your 500 on the bottom. Now here's the thing, guys, you started a parentheses, so we now need to end that first parentheses. Typing that into your calculator, you should get: 0.021. Finding the standard error was all dandy, all right? Finding the standard error, finding that mean was all dandy. But the question is why? Why are we doing this? The "why" we're doing this is ultimately to complete a statistical inference. Do you remember how we learned that word all the way back at the beginning of Chapter 7? Statistical inference. And ultimately, when it came to a statistical inference, we said that it would consist of two parts. It would consist of us making an estimate while also emphasizing that this estimate is not perfect. Emphasizing that we will have a certain amount of uncertainty. Statistical inference is the act of making an estimate while also understanding this estimate is not perfect. It will have a certain amount of uncertainty. And so how do we write out that statistical inference? Well, we first begin with my estimate, what I expect to happen. And that expectation is the mean that we found earlier. So ultimately, that mean we found earlier was that 65%. So notice how we begin our statistical inference emphasizing what we expect to happen. We estimate that mean value we just found. We expect 65% of women to get annual Pap tests. But how are we going to emphasize this uncertainty? Well, we're going to say, "give or take," and "give or take" by what? By that standard error we found in Part B. Give or take: 2.1%. So notice, statistical inference is a two-part process. It's emphasizing both: What do you estimate to happen? Well, emphasizing it's not perfect. So here's a range of what we think it will be. And this, guys, is the start. It's the start of multiple examples of how we're going to do statistical inferences throughout Chapter 7, 8, 9, and 11. But what I reason why I wanted to end with this example in 7.2 is to make you realize calculating that mean, calculating that standard error, is literally the two parts of the process of doing a statistical inference.