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Problem 17 Easy Difficulty

For Exercises $12-21,$ find the margin of sampling error to the nearest percent.
$$
p=67 \%, n=1500
$$

Answer

$M E \approx 2 \%$

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Heather Z.

Oregon State University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Video Transcript

doing a margin of error. Question here. When Ahead wrote the formula. Margin of error is equal to two times the square root of P. P represents the percent of people that are responding a certain way times the quantity one minus P that same P and then divided by n, which is the size of the sample. We're told that RPI is 67% and are in is 1500? That's the knowledge. That's what we need it. So we're good to go, except before we plug in here. We do need to make sure we change that percent to a decibel. You never plug percentages straight into a formula. You change them to decimal form first. The way we change from a percent to a decimal is by dividing by 100. So 67 divided by 100 is 0.67 That's what we're going to use for actual formula. Okay? Meaning If we want to start plugging in here, margin of air is gonna be equal to two times the square root of 0.67 for p 0.67 times the quantity of one minus that same p value 10.67 all of that divided by our sample size R N, which is 1500. Okay, now you need to just plug that into your calculator. Assuming you can plug it into your calculator correctly, you should get 0.24 That's great. That is what we wanted. However, it's not a final answer because we were asked to express our margin of error as a percent. That's just a decimal came. So if a percent changes to a decimal by dividing by 100 than a change of decimal to a percent, Ueda multiplied by 100. Because multiplication is the opposite of division right 0.24 times 100 would be 2.4. Since it asked us to around it to the nearest percent, 4.4 means it would round down. So we would say our margin of error is approximately equal to 2%

University of Central Missouri
Top Algebra Educators
GH
Grace H.

Numerade Educator

Heather Z.

Oregon State University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor