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Problem 6 Easy Difficulty

MEDIA For Exercises 6 and 7 , use the following information. A survey found that 57$\%$ of consumers said they will not have any debt from holiday spending. Suppose the survey had a margin of error of 3$\%$ .
What does the 3$\%$ indicate about the results?

Answer

60$\%$
54$\%$

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Top Algebra Educators
Catherine R.

Missouri State University

Heather Z.

Oregon State University

Caleb E.

Baylor University

Michael J.

Idaho State University

Video Transcript

So on this one, we're being told that 57% of consumers said they will not have any debt from holiday spending. That tells us that we have a margin of error of 3% and asked us what that is representing. Okay, well, what that means margin of error mean error and is to be wrong, essentially arise what that terminology means. So when we're talking about a margin of air, what we're saying is how confident we are Because remember, when we're talking about statistics, we're talking about probability here. They're never gonna be perfect, right? Because if we're saying consumers, there's no way every single person consumer means someone that goes and buys things essentially right. There's no way we can actually pull every single consumer around the entire world. So if they're giving us information from a survey, that survey just took a portion of the consumers. And then we're making a, um, an assumption, a hypothesis, a prediction based off of the small group of consumers we were able to talk to. So when it says 57% of them will not have any debt, that's not a guarantee, right? We don't know it's exactly 57% because we didn't ask every single one of them. So margin of error represents how far off could we possibly be meaning if we're saying that if we're being told that 57% of them said they won't have any debt? The margin of error means you need to add 3% and you need to subtract 3%. 57 minus three is 54 57 plus three is 60. So what the margin of error is telling us is, really, it could be anywhere from 54% to 60% of consumers that will not have any debt. Were not perfectly sure it's 57 but it's somewhere in the range from 54 to 60. That's what margin of error tries to get across

University of Central Missouri
Top Algebra Educators
Catherine R.

Missouri State University

Heather Z.

Oregon State University

Caleb E.

Baylor University

Michael J.

Idaho State University