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Problem 13 Easy Difficulty

For Exercises $12-21,$ find the margin of sampling error to the nearest percent.
$$
p=16 \%, n=400
$$

Answer

$M E \approx 4 \%$

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Heather Z.

Oregon State University

Alayna H.

McMaster University

Kristen K.

University of Michigan - Ann Arbor

Video Transcript

we're being asked to do a margin of error here. So I've gone ahead, round out the formula. Margin of air, as you guys can see is equal to two times the square root of PR percent times the quantity of one minus that same p divided by in our size of the sample. Okay, so it tells me that P is supposed to represent 16% and n is 400. Okay, All we need to do before we start plugging in is fixed that percent. Because we don't plug percentages straight into formulas, we have to change them to decimal form first. The way you change a percentage to a decimal is you divide that percent by 100 16 divided by 100 would be 1000.16 So we're going to use 0.16 and 400 and we're just gonna plug it straight into the formula. So margin of error That is a terrible in good thing I teach math and not English, huh? That is margin of error is equal to to times the square root of RP, which is 0.16 times the quantity of one minus that exact same p 0.16 and then we're going to divide that square. Root extends that. We're going to divide that by our sample size, which in this case, we were told, is 400. Okay, so that is what you're set up should look like. Assuming that you plug that incorrectly to your calculator, Then we should be good. There is a lot to plug in, so make sure you use the parentheses. Make sure you're careful with how you're plugging this in, just like with any other time using a calculator. Okay, Calculators only smartest is operator. So if you plug that in correctly, you should get 0.0 three six. Really? Repeating six is repeating. So we could say 37 But they really won't affect us either way. In the end, um, important thing here, that is a decimal. It asks us to give our answer in percent form. So earlier we went from percent to the decimal by dividing by 100. So if we want to go from a decimal to the percent, we need to do the opposite, which is multiplied by 100 0.36 times 100 would be 3.6 or 3.6, repeating. So then, to write this as the nearest percent, which is what it's asking for, we need to round this to a whole number. Well, 3.6. Since that's higher than point, since this 0.0.5 or higher, we would need to round up, which means this would be approximately 4%.

University of Central Missouri
Top Algebra Educators
GH
Grace H.

Numerade Educator

Heather Z.

Oregon State University

Alayna H.

McMaster University

Kristen K.

University of Michigan - Ann Arbor