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Problem 21 Medium Difficulty

For Exercises $12-21,$ find the margin of sampling error to the nearest percent.
Nine hundred thirty-four of 2150 subscribers to a particular newspaper said their favorite sport was football.

Answer

$M E \approx 2 \%$

Discussion

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Video Transcript

So this is a margin of error question here. Uh, that means we're gonna be using this formula, which is margin of error equals two times the square root of P, which will be our percent times one minus that same p divided by end the size of our sample. Which means in order for me to be able to solve this out for us to be able to solve this out, we're going to need a P, and we're gonna need an end. Okay. P is supposed to represent the percent of people that responded a certain way. And N is supposed to represent the size of the sample, meaning the total people total whatever serving total stuff that we used. Usually it's the people surveyed that's gonna be the size of our sample. We're looking at my problem here. We're told the 934 of 2150 subscribers responded whatever to a particular newspaper said their favorites for was football doesn't really matter what's about right, and it could be anything. So the total looks like is 2150 subscribers, right? That's the total number of people that were apparently asked about their favorite sport. So that's going to be our end and is always gonna be the total number of people in the sample. Okay, the question then is what is P? What is the percent? Because I'm not being shown a percent here. Well, we're gonna have to find the percent ourselves. Okay, Percent is just another way of representing a decimal or a fraction. And we find that by doing part over whole right, we find a percent by part overhaul. If you got a, you know, 80% on a test. That means you roughly gotten eight out of 10. All right, you didn't. You got 80% out of the full 100% you possibly could have got. So if we've been told that 900 change the color that 934 people out of the 2150 answered a certain way answered, the football is their favorite sport. Let's figure out what percent of the total that 934 is right. So the way to do that is just what I've written here. Take 934 divided by 2150. If you do that, you get zero point 43 That's what you get. 0.43 meaning. Remember that this is decimal form. If you want to think of this as a percent, you'd multiply that by 100 which means this represents 43%. 43% of the people that were surveyed apparently said that football was their favorite sport. But really, 0.43 is what we wanted anyways, right, because any time we have a percent before we plug it into the formula, we have to change it to a decimal anyways. So 0.43 is what we really wanted, because that's what we're gonna plug into the formula meeting. Now. I can solve this out by setting up the formula. Same margin of air is equal to to times the square root of P. My percent of people that answer a certain way. And it turns out that 0.43 or 43% of the people said football was their favorite sport. Then I'm going to take that times the quantity one minus that same percent of 10.43 and then we're gonna divide all of that by the total number of people surveyed the size of our sample, which in this case was the 2150 subscribers, sir. Now, you just need to plug that into your calculator, See what we end up getting, because that's gonna give us our margin of air if you plug this into your calculator correctly, which again feel forget a positive video and plug it in to make sure you can do this yourself, because you may not be a little plug it and quite that fast. But if you plug it in correctly, you should get 0.21 Now that's a great That is our margin of error, but we were asked to put it in percent form for answer. So we have a decimal. The way you change a decimal to a percent is multiplying by 100 0.0 to 1 times 100 would give me 2.1% so it around that to a whole number. Like what it's asking for the nearest percent. We would say our margin of air is approximately equal to two percent since the 0.1 means it would round down

University of Central Missouri
Top Algebra Educators
GH
Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University