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Problem 15 Easy Difficulty

For Exercises $12-21,$ find the margin of sampling error to the nearest percent.
$$
p=48 \%, n=1000
$$

Answer

$M E=3 \%$

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Top Algebra Educators
Heather Z.

Oregon State University

Alayna H.

McMaster University

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor

Video Transcript

doing a margin of error problem here. So we're told that we've got a p of 48% and we're told that we have an n of 1000 of gone ahead and written out the formula for margin of error Appear your margin of air is equal to two times the square root of P, which is your percent specifically is the percent of people that are responding Teoh, whatever we're talking about in this case, um, then you have times the quantity of one minus that same p divided by n, which is the size of your sample. Okay, so in that case, then we know we can't use 48 as our actual number because that's the percentage form. What we need is to turn this into decimal form came so to change percent to a decimal, we need to divide by 100 48 divided by 100 would give us 1000.48 So now that we've established that, we can actually start plugging stuff into our formula. So our margin of error Emmy is gonna be equal to to times the square root of P, which we've established his 0.48 then times D quantity of one minus that exact same p 10.48 And all of that is gonna be divided by our sample size of 1000. Not 100 but 1000. OK, so then you just need to be able to plug that into your calculator correctly. If you are able to plug in your calculator which feel, forget a pause this video and take your time to plug it in to make sure you can do it yourself. If you plug it into the calculated correctly, you should get 0.3 Okay, now that's great. That is correct. If you get that, however, that's not our final answer because it wants us to write our answer in percentage form. Well, if dividing by 100 changes a percent to a decimal than the opposite way multiply and by 100 should change a decimal to a percent right. Works both ways. 0.3 times 100 would be three. That's a nice round number. That's exactly what we want. So we just say our margin of air is approximately equal to 3%

University of Central Missouri
Top Algebra Educators
Heather Z.

Oregon State University

Alayna H.

McMaster University

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor