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Problem 16 Easy Difficulty

For Exercises $12-21,$ find the margin of sampling error to the nearest percent.
$$
p=33 \%, n=1000
$$

Answer

$M E \approx 3 \%$

Discussion

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Caleb E.

Baylor University

Video Transcript

So we're doing a margin of error Question here. I've gone ahead and written out the formula. Margin of error is equal to two times the square root of P. P represents the percent of people that are responding in a certain way. Uh, then it's times the quantity of one minus that same p divided by n, which is the size of the sample. Okay, so we're told that P represents 33% and then we're told that n represents 1000. Well, the only catch here is we can't actually use 33 in our formula. Okay? We don't use numbers in percent form and actual formulas. We need to change them to decimal form first. The way you change a percent to a decimal is dividing by 100 33. Divided by 100 gives us 0.33 Okay, so that's what we want to use. So now we're gonna plug stuff in here. Margin of air is gonna be equal to two times the square root of RP, which is 0.33 Because we established me to make that a decimal times the quantity of one minus that exact same p. So again 10.33 that all of that is going to be divided by R N R. Sample size, which is 1000 now. It's really about Can you plug in your calculator correctly so feel Forget positives video If we need to take your time to actually test yourself to see if you can plug this into your calculator correctly because that is a useful skill. If you plug it incorrectly, you should get 0.29 Okay, that is the desperate answer. If we look at the directions, we were asked to give a percent. So in this case, if dividing by 100 changes a percent to a decimal than multiplying by 100 should change a decimal to a percent point. Haute 0.29 times 100 would be 2.9. Well, we were asked to give to the nearest percent. So then, for our final answer, our margin of air would be approximately equal to 3% because we would need to round the 2.9 up to get ourselves a nice hole number. That would be your answer

University of Central Missouri
Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Caleb E.

Baylor University