Like I mentioned to you guys already, we are going to go through these examples of California community colleges and that parent example over and over again. So let's just read the example one more time just to refresh our memory on it. The statewide success rate in math for all California community colleges was just 54% in Fall 2010. Over the next decade, the math department at West Valley College tried various methods to improve learning. In Fall of 2020, a random sample of 200 West Valley math students were surveyed, and of these students, 133 were successful in their math class. Is the success rate in math for all students at West Valley significantly higher than the statewide success rate in Fall of 2010? Again, what do I want to do here? I want us to find the one-proportion Z-test statistic. To do that, let's just go back and recall what was the hypothesis I wrote down for this? Remember, the hypothesis will consist of the null P is going to be equal to that status quo value of 54%. That was the statewide success rate; that was the historical success rate. And ultimately, we are going to be comparing West Valley P (West Valley success rate) to that status quo. In particular, we are looking at a significantly higher statewide success rate. And so remember, "significantly higher" is what emphasized greater than. And so what I want us to do is ultimately plug into the Z-test statistic formula. Alright, I want us to plug into this formula. And ultimately, what I want us to see here is that we are going to need different values in this formula. Notice, first and foremost, we're going to need that P value, which luckily we already found. We already found that the status quo is 0.54. But notice what else we need in this Z-test statistic. It's ultimately p-hat and n. Notice p-hat and n are both values from your sample. And so when it comes to doing these problems, you're also going to need to identify the number of successes and the sample size for your sample. Now let's remember, number of successes and sample size are going to be given to you. We can see here in the prompt we ended up taking a sample of 200 West Valley students. So again, 200, we were given the sample size of n, and successes, successes are literally how many students successfully completed their math class. We can see here we were also given the x value, 133. And it's these two numbers, 133 and 200, are then what we use to find the sample proportion, which is x divided by n. Remember, we learned how to find a sample proportion all the way back in Chapter 1, Section 1.4. And so we can find that x/n = 133/200, or as a decimal, that's 0.665. And that ultimately, these are the values we then plug into the Z-test statistic formula. We take that value of 0.665 and we're going to subtract that by my status quo value of 0.54. And then we are going to divide that by the square root of P⋅(1−P)/n. Noticing how it's following the z-score pattern, comparing my sample proportion to my status quo, and then dividing by that standard error spread value. Now, who feels like typing this into your calculator? Who here feels like plugging this in, versus who here feels like not doing it? Yeah, no, alright, let's not type this into our calculator. Alright, why did I have us do this formula? Alright, I had us do this formula because I wanted you guys to see the two key ideas that come into play in it, literally in color. In the Z-test statistic formula, we're using blue (status quo) and orange (information from my sample). And that's really all you need to know to find the Z-test statistic. This formula will be the same every single time. So, wouldn't it be great if my calculator could just eat those important values and then spit out the Z-test statistic? Why yes, yes it does, and that is what I want you guys to do on the exam. Not on the exam is going to be this crazy formula. Rather, what I want you to do for the exams is to compute the one-proportion Z-test statistic using your graphing calculator. And what you're ultimately going to see is that it's literally going to spit out this exact value for us. So let's do it together. I want us to go to Stat, go to the Test column. Again, it's exactly where we went in Chapter 7 doing confidence intervals, except now we're going to choose the function One Prop Z-test. Why? Well, we're still looking at one population. We're still only looking at West Valley students, one population. We're still looking at proportions, meaning we're looking at the percent who passed their math class. And then Test, well, Test is simply because we are running a hypothesis test. And so I want you guys to see that the name of the test function we're going to use, One Prop Z-test, is intentional. It's intentional because Test is emphasizing hypothesis test. And when you guys click into One Prop Z-test, I want you to note the three things it's looking for: the status quo; the number of successes; and the sample size. I want you to see that ultimately, when it comes to using your graphing calculator to calculate the Z-test statistic, the three values it wants you to plug in are the exact three values we needed to plug into the formula. You need P_0 = 0.54; you need the x, the number of successes, because that's the top of the fraction (133); you need the n value, 200. And if we plug these values in, let's do it together in our calculator. All we have left to do then is pick the correct inequality, and even that has been already identified for you. You already identified in the alternative hypothesis we're using the greater than symbol. So pick the greater than symbol because that's ultimately the inequality my alternative hypothesis is telling me to use: >. And if you guys hit calculate, bam, you're going to get two numbers displayed out in front of you where that first number that starts with the letter Z is quite literally the Z-test statistic. So instead of plugging this really ugly algebraic expression into your calculator, you just hit Stat, Test, One Prop Z-test, plugged in a few numbers, picked the correct inequality, and bam, it gave you the Z-test statistic of positive 3.55. Tell me, which one would you rather do? Would you rather do the graphing calculator function or would you rather type in that ugly expression? Which would you prefer, the ugly or the calculator? We absolutely would prefer the calculator option. Absolutely, that is how we calculate the Z-test statistic. Underneath that, I want you to see that there's another number there. It starts with the letter p. That's going to be the p-value, which we're going to actually discuss a little bit later. But let's just write that number down right now. Some of you might have it written out nicely as a decimal like that. Some of you might have it written out as 1.94e-4, and remember, that's just scientific notation. So in this case, it's giving us 0.194. Just write that number down, and we're going to come back to it in a little bit.