WEBVTT
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this question wants us toe make 200 samples of size
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10 from the normal distribution. Now, you can
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see that I'm not on the white board. In
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fact, I'm using a programming language called R.
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R. Is a statistical programming language that's perfect for
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stuff like this creating a bunch of samples of random
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variables. Um, So what we're gonna do is
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I am using a for loop to make 200 samples
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. The way I'm gonna sample from the normal distribution
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is I'm gonna use this function are norm which create
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which will create random numbers from the normal distribution that
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would give it It will create 10 random numbers of
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vector of 10 random, normal numbers and it will
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take it from the normal distribution with a mean it
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100 a standard deviation of 20. Just like the
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question asked us to do. So let's go ahead
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and run this and it will quickly create 200 samples
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each of length 10 weaken. Take a look at
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this and it will see that we have here a
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list of 200 samples and each element in this list
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is a sample of like 10 so now, it
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also the question asked us to find the mean of
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each sample. To do this, I'm gonna use
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this function that will find the mean of every element
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in our list of samples. So we'll do that
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. And now we have a vector of length 200
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that has sample means for each, uh, interest
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sample in our list of samples. Finally, it
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asks us to plot all of these sample means in
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a hist a gram. So using the function hissed
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will go ahead and do that, and we can
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see that this is the resulting distribution. So let's
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go ahead and describe this sampling. Distribution of sample
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means we can see pretty clearly that it's centered around
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probably around 100 or somewhere a little bit less than
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100. It's clearly, you know, motile it
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only has one peak, and it seems to be
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pretty symmetrical. It might be skewed a little bit
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toothy left that is ahead a little bit longer tail
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on the left than does on the right. But
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we don't really have enough evidence for that. It
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looks pretty symmetrical, so we can say its image
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. This, uh, distribution also has a range
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from what seems like 80 to 1 15 So we'll
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say that it's uniforms symmetrical, centered around 100 with
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a range of 80 to 1 15 And that is
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the description of our sampling distribution of sample means.