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Problem 1 Medium Difficulty

Determine whether each situation would produce a random sample. Write yes or no and explain your answer. the government sending a tax survey to everyone whose social security number ends in a particular digit

Answer

Yes this is random sample
Reason: The last digit of the social security numbers given by the government tax survey is always a random since the numbers lie between the digits 0 to 9 .

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Top Algebra Educators
Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Caleb E.

Baylor University

MG
Maria G.

Numerade Educator

Video Transcript

So when we're being asked to determine if some situation would produce a random sample to me, there are two main questions that we want to be asking ourselves. First is how are we picking people for this study or survey? You know, what group of people are we picking from that sort of thing? Second question is who or what is the study supposed to represent? Because the way we know if we have a random sample is if whatever this study is supposed to represent, whatever group of people this study is supposed to represent, do all the people in that group have an equal chance of being picked for this study? If all the people in the group that were supposed to represent having equal chance of being picked, then yeah, it will be a random sample. Okay, So for example, take this problem. We're saying that the government is sending a tax survey out to people whose social Security number ends in a particular digit. So to the question of how were people being picked for this study? Well, the way people are being picked is by their social security number. All right, that's what we're told off this. The way people are being picked is based off their social Security number. Okay, so then the question is, who or what is this study is supposed to represent? Well, it looks like the government is sitting out this survey to ask people about taxes, meaning if we're asking who this is supposed to represent, this is supposed to represent people who pay taxes, people who pay taxes. Excuse my handwriting. I am a mathematician not known for the best handwriting, you know. So if we look at this, then the question when you'd ask ourselves is if this study is about people who pay taxes, is picking people from their Social Security number going to give everyone that pays taxes an equal chance of being picked? Well, if you know how taxes work, the way you pay taxes is by your Social Security number. If you haven't filed taxes before, when the time comes when you file taxes, what you're gonna first thing you're gonna have to give them. Besides, your name is going to be your Social security number. Every person that has a social security number has to either pay taxes or prove that they haven't made enough to pay taxes, which is where some of you may be at this point. So for this problem, the answer is yes. This would be a random sample. Yes, this is a random sample, and the reason for that would be since we're picking off a Social Security number. Everyone that pays taxes should probably capitalized that everyone, everybody. Now everyone would work better. Everyone that pays taxes, which again, is what this survey is about. Everyone that pays taxes has an equal chance of getting picked or will say, getting surveyed, since the question specifically states that they're sending out a survey. Okay, that's the idea. The study was about people who pay taxes and if you choose Bill by Social Security number, anyone that has a social, everyone that pays taxes has a Social Security number, so you have an equal chance to get any single person that's ever paid taxes. That's why it's random

University of Central Missouri
Top Algebra Educators
Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Caleb E.

Baylor University

MG
Maria G.

Numerade Educator