For Exercises $3-5,$ find the margin of sampling error to the nearest percent.
p=72 \%, n=100
All right, so we're doing margin of error today. I have gone ahead and written out our formula for margin of error. So m e represents the margin areas. You can see their P represents our percent. That will be given, um, and then R N represents the size of the sample meeting. You know, if we're talking about, uh, people, how many how many people are in the in the sample? Gripper, that, remember, sample is a term for for this purpose. That means you're your group that you are pulling or the group that you are studying. Whatever, Whatever this. Whatever this study is over. When we talk about the sample, we're talking about two people or the objects that you are talking to studying that sort of thing. OK, so then we've got our formula down here, which is that margin of error is equal to two times the square root of our percentage times the quantity one minus that same percentage. It is the same percent in both places. That's why it's p in both places, divided by n, which is our size of their sample. Okay, um, one big thing to make sure you recognize p specifically says it represents the percent meaning in the problems we have, it's going to be giving us a percentage, but we know that we don't plug percentages straight in to an equation. We have to change them into decimal form first, Right? We've talked about percent. Per is a term. That means division in math sent is a prefix for 100. So percent literally means divide by 100. Meaning if we take a look at number three here, we're told that our percent is 72. All right, we're told that p equals 72%. Well, we're not gonna plug 72 into our equation. What we are going to do is take 72 divided by 100 to give us. It's a bad equal sign to give us 1000.72 That is the decimal that we will be using to actually plug into the formula to the equation now in when they tell us and equals 100 is exactly what they say it is. So when they tell us and equals 100 that means we're gonna be plugging 100 into the formula. Okay. Other thing to recognize is that it is asking us to find the margin of error to the nearest percent, meaning when we get done with our formula here, the answer we get will be in decimal form. We will have to change it back. 2% meaning, yes. We're starting our problem off by taking 72% divided by 100 changed into a decimal. And we're going to end by having to take whatever our answer is and multiply it by 100 to get back to being a percent feels kind of annoying, But that is what we have to do here. All right, let's plug into the formula. So we're trying to find the margin of error, which we don't know yet, and that is gonna be equal to two times the square root. We know that our percent is 0.72 times the quantity times the quantity of one minus again, that same percent. So 10.72 and then all of that is going to be divided by our sample size n, which is 100. That right there would be your formula. Okay, Two times the square root of 20.72 times the quantity of one minus 10.72 divided by 100. If you've got that part figured out, the rest was just throwing into the calculator. So we take it and we go throw it into our calculator. Assuming that you plug it in correctly, you should get 0.0 eight nine and junk. Okay, again, that is not our final answer. That is our decimal form. The question is very clear. It asks for it to the nearest percent. So since this is our decimal form, now we need to multiply this by 100 or, in other words, move the decimal 1000.2 places to the right to change it to a percentage. Well, if you multiply this by 100 you would get 8.9, right? Well, right over here. If we multiply this by 100 we would get 8.9 percent. So we'll just go ahead and round that off to a nice hole number and we will say our margin of error is equal to nine percent