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Margin of Error

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This tutorial covers margin of error. Before we tag what margin of error, let's review a bit. The population is the complete set of things to be studied. The sample is a subset of that population. When we take an estimate, we're talking about a rough calculation.

It's an approximation. It's an inference about the population. An inference is kind of like a hypothesis. It's an educated guess based on information we have, so we're trying to make some educated guess based on information that we have about our population.

Now that information, that comes from our sample. So whenever we take a sample, we're trying to estimate something about the population. We're trying to draw an inference about that population. Because we're only looking at a subset of the people, we're not looking at everyone, there's going to be some error. There's bound to be uncertainty.

The margin of error helps us to quantify that uncertainty. It tells us how far away from the population our estimate can be. The confidence interval uses both of those pieces. It uses the margin of error, as well as the estimate. When we combine them, it gives us a range of possible values that our estimate can be.

So this confidence level tells us how sure we are that our interval contains the actual population value, how sure we are that our sample falls in that range. Here's an example of several confidence intervals. First, our population. Our population has a value of 60%, so 60% of our population believe something.

We take 50 different samples all from that same population. Each time we take a different sample, we get a different subset of people, so each sample is going to be a little bit different. That's why there's this variation. These blue lines show the confidence interval.

We are saying that we are 90% confident that the population falls within this estimate, and how large the bars are depends on the margin of error. So here, most of these samples do end up containing the population. However, there are a handful-- there's one right here, right here, here, here, and here. --that show where the confidence interval does not contain the population value. So sometimes, even though we're doing samples, even though we're doing lots of samples, some of them are not going to end up containing the population value. And that's OK.

That's the reason we're using a confidence interval, because we're not 100% sure. We're only 90% sure, so we would expect that some of the times when we take a sample, the sample that we take is not going to be perfect. It's not going to contain the population value. This is has been an introduction to the margin of error and confidence intervals. Confidence intervals are explored in much greater depth in another tutorial.