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# For Exercises $12-21,$ find the margin of sampling error to the nearest percent.$$p=81 \%, n=100$$

## $8 \%$

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you're doing margin of error here. Gone ahead and written out. The formula for margin of their margin very is equal to two times the square root of p, which is gonna be your percent times the quantity of one minus that same p divided by n which is your sample size? Okay, Um very nice of them on this problem. They are very straightforward. They tell us specifically that P is equal to 81% and then they also tell us that N is equal Teoh 100. So we don't have to go searching through a problem that just tells us that that's awesome. One key thing here Do you recognize that they give us P as a percent, which is what they're supposed to do? It is up to us to adjust that before we plug it into the formula. Because we do not plug percents into formulas, we have to change them into desperate form. First percent is a term that means divide by 100. So if you want to change a percent to a decimal, you just divide by 100 81. Divided by 100 is 1000.81 That's what we will be using for this formula. Okay, so now to plug in Sorry. Now to plug in, we're going to have our margin of air. It's gonna be equal to to times the square root of RP, which we have found his 0.81 If we're gonna plug it in the correct fashion, then we're gonna take that times the quantity of one minus p, which is one minus 10.81 Peace the same in both cases, right? And we're gonna divide that by n our sample size, which is 100. That would be what you'd want your formula to look like before you start plugging into your calculator. As long as this part makes sense, where we got me, what? They gave us those two variables, and then I just plug them in. So as long as you're good with where those air plugged in it, you throw it into your calculator and the rest is gonna be up to it. Really, if you throw this into your calculator correctly, you would get 0.78 That's great. But it asked us to find the margin of error to the nearest percent. This is just decimal form. We want our actual percentage answer well. If going from a percent to a decimal is dividing by 100 then going from a decimal to have percent the other way would just be the opposite. Multiplying by 100 0.78 times 100 is 7.8. So by the rules of rounding, then if we're going to the nearest percent, if it's 7.8, that means we would round up to say our margin of error is approximately 8%.

University of Central Missouri