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Problem 25 Medium Difficulty

PHYSICIANS In a recent poll, 61$\%$ of the 1010 people surveyed said they considered being a physician to be a very prestigious occupation. What was the margin of error?

Answer

$3 \%$

Discussion

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Top Algebra Educators
Catherine R.

Missouri State University

Alayna H.

McMaster University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Video Transcript

So we've got a margin of error question here. Um, we mean because we're going to be asked if on Marcia there went ahead and wrote down the formula. Margin of error, as you guys can see, is equal to two times the square root of P represents the percent times the quantity of one minus that same p divided by n, which represents our sample size. Okay, so in order for us to find this margin of error, we're gonna need to figure out what P is and what in is Well, it tells me that 61% of the 1010 people surveyed said blah blah, blah, blah, 61%. That's gotta be p cause P is gonna be represented as a percent and is represented than the total number of people in our sample, which in this case, would be the 1000 and 10 people that were surveyed. Okay, so the only catch years that we can't use 61 for R P because we don't pluck percentages straight into a formula. We need to change them into decimal form first. Then we can plug them in the way you change a percent to a decimal is dividing by 100 61 divided by 100 would give us 1000.61 Now we are ready to plug into the actual formula. So margin of air is gonna be equal to two times the square root of RPI value, which is 0.61 we said times one minus that exact same P value of 10.61 And then all of that is going to be divided by our sample size R N, which is 1000 and 10. So really, the rest of this comes down to Can you plug into the formula correctly? Can you plug this into the calculator correctly? I mean, if you plug this into the calculator correctly, you should get 0.31 because it's 306 so that it would round 231 right? That's a great decimal answer. We need to just change this 2% form to get our final answer. So if we have a decimal, the way you change a decimal to a percent is by multiplying by 100 0.31 times 100 I would give us 3.1% and So then, to put that as a whole number, we would say our margin of air is approximately equal to three percent.

University of Central Missouri
Top Algebra Educators
Catherine R.

Missouri State University

Alayna H.

McMaster University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University