so in this video let's take a look at this problem and a simulator which we got from statcrunch so this is an applet in statcrunch you can get to it yourself if you want to in the applets menu and then choose sampling distribution i went ahead and set the mean of the population to be 3500 because that's what we're told in this problem and i went ahead and assumed the standard deviation was 100. the problem says that we're going to collect a sample size of size nines i'm going to also change this from a 2 to a 9 for the sample size so let's take a look at what we have up here at the top we have a picture of the distribution of the population this second graph in the middle is going to represent individual samples of size nine and then this third graph on the bottom is going to be a graph of the sample means so in other words when i click this button that says one time right here it's going to take one sample of nine and then it's going to take the average or the mean of those nine items calculate the the average and then plot that down here on the sample means graph so let's do it once what you're going to notice is that when i click the button one time you'll see nine randomly selected data points from the population so that would be nine randomly sampled babies and they're going to drop individually here onto the samples once nine of them have been completely randomly selected then you're going to see a green box which is the mean of those nine drop down to the bottom one so let's do that once and see what happens there's the nine once nine are selected then you can see that green mean which is right here has been graphed so this represents nine babies this represents the sample of nine babies that we just saw if i do it again one more time it's going to clear these nine randomly selected babies select nine more and continue that process computing the mean but it's going to drop a second sample mean down at the very bottom so let's do it one more time here come nine randomly sampled babies from the population and there's the mean of that sample of nine so if i continue to do this multiple times what we're going to see is many sample means being plotted on this graph below i can do it five times and that's going to take a while because of the animation so you sort of have to be patient but you can see that it's going to take five samples of nine babies so let's let that go ahead and finish and notice that what's happening down below is the distribution of the sample means down below is starting to be built now we don't want to do that repeatedly one or five times because of the animation let's just do it 1000 times so what this means is we're going to take 1 000 different random samples each of size 9 and then calculate 1 000 sample means and plot those 1 000 sample means down here let's do that okay that did it very quickly because it's not going to animate it for me what you actually now have in this graph is a graph of 1007 samples and you can see that if you took the mean of all of those samples in other words the mean of the means it's about 3498 very close to the mean of the population and the standard deviation is 33.82 which is very different than the standard deviation of the population and you can do this as many times as you want right now i have 1007. if i do it again now i have 2007 and i can do that a bunch of times let's go to 10 000 different samples notice the mean is still very close to the population mean and notice the standard deviation has stayed different from the standard deviation of the population