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Dialogue: 0,0:00:00.20,0:00:05.11,Default,,0000,0000,0000,,Now remember what we are originally trying to find. We're trying to find where
Dialogue: 0,0:00:05.11,0:00:10.58,Default,,0000,0000,0000,,on the distribution of sample means a particular sample will lie. Not just for a
Dialogue: 0,0:00:10.58,0:00:15.49,Default,,0000,0000,0000,,simple population like this one, but for a huge population. And now we can do
Dialogue: 0,0:00:15.49,0:00:20.88,Default,,0000,0000,0000,,that. Because now we know that the distribution of means, where every mean is
Dialogue: 0,0:00:20.88,0:00:26.71,Default,,0000,0000,0000,,the mean of a sample of size n. This distribution has a standard deviation equal
Dialogue: 0,0:00:26.71,0:00:31.99,Default,,0000,0000,0000,,to the population standard deviation divided by the square root of n. This is
Dialogue: 0,0:00:31.99,0:00:36.82,Default,,0000,0000,0000,,called the central limit theorem. And it not only holds true for these simple
Dialogue: 0,0:00:36.82,0:00:42.78,Default,,0000,0000,0000,,populations but for any population. Because of the central limit theorem, we can
Dialogue: 0,0:00:42.78,0:00:47.28,Default,,0000,0000,0000,,have a population of any shape. And then let's say we draw a sample from it and
Dialogue: 0,0:00:47.28,0:00:51.25,Default,,0000,0000,0000,,calculate the mean, and then we draw another sample from it and calculate the
Dialogue: 0,0:00:51.25,0:00:57.88,Default,,0000,0000,0000,,mean. And we keep doing this, say a 100 times. Assuming the sample size is large
Dialogue: 0,0:00:57.88,0:01:02.44,Default,,0000,0000,0000,,enough, if we plot the distribution of means, we're going to get something
Dialogue: 0,0:01:02.44,0:01:07.44,Default,,0000,0000,0000,,that's relatively normal. With a standard deviation equal to the population
Dialogue: 0,0:01:07.44,0:01:12.90,Default,,0000,0000,0000,,standard deviation divided by the square root of the sample size. And we've been
Dialogue: 0,0:01:12.90,0:01:18.65,Default,,0000,0000,0000,,calling it SE so far. And that's because this is called the standard error. This
Dialogue: 0,0:01:18.65,0:01:24.33,Default,,0000,0000,0000,,is super cool, but I also understand that it's also super complicated. So we're
Dialogue: 0,0:01:24.33,0:01:28.89,Default,,0000,0000,0000,,going to go through a few more ways of looking at this, using applets and
Dialogue: 0,0:01:28.89,0:01:33.75,Default,,0000,0000,0000,,demonstrations. And then finally at the end of this lesson, go over an example
Dialogue: 0,0:01:33.75,0:01:36.46,Default,,0000,0000,0000,,where we would actually use this in real life.