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Problem 14 Easy Difficulty

For Exercises $12-21,$ find the margin of sampling error to the nearest percent.
$$
p=54 \%, n=500
$$

Answer

$5 \%$

Discussion

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Caleb E.

Baylor University

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor

Video Transcript

doing margin of error here. I've gone ahead and written out the formula for margin of air. Uh, you've got two times the square root of P. Whatever percent your given times, the quantity of one minus that same p divided by n the sample size. Okay, so it tells us that r p is 54% and that are in is 500. Okay, so if that's the case, we don't want to pluck 54 into our formula because we know we're not supposed to plug percentages into our formula. We need to divide 54 hopes. Forget to change my color. We need to divide 54 by 100 to figure out what that is in decimal form. While 54 divided by 100 is 1000.54 That's what we will be using to plug into the formula. Okay, so our margin of air I m e is gonna be equal to two times the square root of RP, which we just established his 0.54 times the quantity of one minus that exact same p again. And all of that is going to be divided by R N r sample size, which is 500 apparently. Okay, as long as you plug that all into your calculator correctly, you should be able to come up with the correct number. If you plug that into your calculator, you will get 0.45 Okay, I say that because it's 0.445 So if you look that if we're rounding the three numbers or if you condone, just even go a bit further if you need to. But either way, you would need to round that up because of the five. OK, well, we weren't asked to give a decimal answer, though. If we look at the question and it tells us to write our answer in percentage form. So if we want to change from percent two decimal, we divide by hundreds. If we want to change from decimal 2% we multiplied by 100 so that means we would have 4.5. Rounding them to the nearest percent means we would just barely have to round up to give us 5% for margin of air

University of Central Missouri
Top Algebra Educators
GH
Grace H.

Numerade Educator

Caleb E.

Baylor University

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor