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