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# For Exercises $3-5,$ find the margin of sampling error to the nearest percent.$$p=31 \%, n=500$$

## $4 \%$

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So we're doing margin of error here. I've kind of head and written out the formula here. The margin of air is equal to two times the square root of P, which is the percentage that we're going to be given, uh, then times the quantity of one minus that same p divided by n which is our sample size. Okay, In this problems case, we don't even have to search for that information. It's just straight up telling us what P and N are. So that's very nice of them. Do make sure you remember that whenever the problem tells you here that P is equal to 31% that is useful information. But that's not what we're actually going to plug into the formula. We don't plug percentages straight into a formula ever in math. We always need to change it back to decimal form. Okay. Meaning. Remember, that percent literally means divide by 100. So if you ever want to change a percent to a decimal divide, that number by 100 31 divided by 100 is 0.31 That is what we're actually gonna be plugging in for Pete, meaning that what we should be setting up here is that our margin of air is gonna be equal. Teoh to times the square root of 0.31 times de quantity of one minus again 10.31 And all of that is gonna be divided by our sample size R n, which we're told is 500. That is what you're set up should look like for this problem. Okay? Just plugged in 0.31 for P and then plugged in 500 friend. Besides that, go to your calculator, and you just got to make sure you plug that incorrectly. If you plug that incorrectly. What? You should get ups. Forgot to change color again if you plugged it incorrectly. What? You should get zero point 041 Okay, that is your decimal answer. But if you look at the question, it asked you to give it to the nearest percent. We're looking for a percent answer. So the same way that to change the percent to a decimal we divided by hundreds right up here. If we want to get our decimal to a percent, we need to go the opposite direction. We need to multiply this by 100 if you take 0.0, for one times 100 you would get 4.1. So just round this off to the nearest percent. Meaning no decimals or anything like that. Our margin of error. Since it's just 4.1, we would round down and say that our margin of error is approximately equal to a simple nice 4%.

University of Central Missouri