Comparing and sampling populations
City Councilwomen Kelly wants to know how the residents of her district feel about a proposed school redistricting plan. Which of the following survey methods will allow councilwomen Kelly to make a valid conclusion about how residence of her district feel about the proposed plan? So before we even look at these, we just have to realize that if you're trying to make a valid conclusion about how the residents of her entire district feel about the proposed plan, she has to find a representative sample, or not kind of a skewed sample that would just sample parts of her district. So let's look at her choices. Should she just ask her neighbors? Well, she might live in a part of the neighborhood that might unusually benefit from the redistricting plan or might get hurt from the redistricting plan. And so just her neighbors wouldn't be representative of the district as a whole. So just asking her neighbors probably does not make sense. Ask the residents of Whispering Pines Retirement Community. So once again, the first one skews by geography. She's oversampling her neighbors and not the entire district. Here, she's oversampling a specific age demographic. So here she is oversampling older residents who might have very different opinions then middle aged or younger residents. So that doesn't make sense either. Ask 200 residents of her district whose names are chosen at random. Well, that seems reasonable. It doesn't seem like there's some chance that you somehow over sampled one direction or another. But it's most likely to give a reasonably representative sample. And this is a pretty large sample size. So it's important to say, what is the random process, where she getting these names from? But this actually does seem reasonable. Ask a group of parents at the local playground. Well once again, this is just like asking your neighbors. And it's also sampling a specific demographic. Now, this might be the demographic that cares most about the schools. But she wants to know how the whole district feels about the redistricting plan. And once ago, this is at a local playground. This isn't at all the playgrounds in the district somehow. So I wouldn't do this one either. Let's do one more of these. Mimi wants to conduct a survey of her 300 classmates to determine which candidate for class president-- Napoleon Dynamite or Blair Waldorf-- is in the lead in the upcoming election. Mimi will ask the question, if the election were today which candidate would get your vote? Which of the following methods of surveying her classmates will allow Mimi to make valid conclusions about which candidate is in the lead? So let's see, ask all of the students at Blair's lunch table? No. That would skew it in Blair's favor, probably. That's not a representative sample. Ask all the members of Napoleon's soccer team? No, same thing. They're likely to go Napoleon's way or maybe they don't like Napoleon, maybe they'll go against Napoleon. But either way this seems like a skewed sample. Put the names of all the students in a hat and draw 50 names. Ask those students whose names are drawn. Well this seems like a nice random sample that could be nicely representative of the entire population. Ask all students whose names begin with N or B? Well, this could be perceived as kind of random. But notice, N is the same starting letter as Napoleon, B is the same starter letter as Blair. You might say, well, that's fair. You're doing it for each of their letters. But maybe there's like 10 people whose names start with an N and only two people whose names start with a B. Once again, you're not even getting a large sample. And then on top of that, maybe there's some type of people with the same starting letter somehow like each other more. So I would steer clear of this one. Ask every student in the class? Well, that would work. There's 300 classmates, that might not be that time consuming. You can't get a better sample than asking everyone in the population. Which of the following methods of surveying our class which will allow Mimi to make a valid conclusion about which candidate in the lead? Well, that's a pretty good conclusion. People might change their mind. So it's not a done deal. You can't get a better sample size then the entire population. Assign numbers to each student in the class and use a computer program to generate 50 random numbers between 1 and 300. Ask those students whose numbers are selected. Well this is pretty close to put the names of all the student in a hat and draw 50 names. So I would give this one. That seems reasonable as well.