 Welcome back to another video on confidence intervals and bootstrapping. Where we left off, we developed this plot to show our confidence interval using the bootstrap sampling distribution. We're going to continue to build up that plot, but we're going to use the original samples. And so the process of calculating the confidence intervals is still the same. I'm going to create XBD for X-bar data. And we're going to use the data means, which if we scroll back up here, data means has our original four samples and those sample means. And so we want a mean of those four samples. And I won't do any fancy printing here and just show you what the thing is I had a typo again with the capitalization have to make sure it's exact. But we can see this is what our data X bar is. Similarly, we can calculate the standard error with data means. And so here we can see, oh, I forgot my parentheses there. And so we can see a single value here for our data standard error. And then we can calculate the confidence interval SID. So here we would say XBD minus two times SED and then XBD plus two times SED. And so here we have our basic confidence interval for the data. We can build up this plot. So once again, I'm going to copy this. I'm going to bring it down here and run it again to show you what we had before. And so now we want to add in the data confidence interval. And again, we have this geom error bar HAS. We'll put this down a little lower. So we'll put it at 0.25. We still need to say X min is CID at the zero index and X max is CID at the one index. And then outside the AES we'll say color is, we'll make it green. And I'm going to add in an extra term called height. And this tells it how high we actually want the error bar to be. So it defaults to 0.5. So this is going from 0.25 to 0.75. I'll shorten this one so that it's 0.25. And then we also add the point at the middle, making sure that our Y matches up. So 0.25. And our X is at XBD. Our color is the same green. And we'll make it size three. So if we run this, we can now see that we've got the confidence interval based off of the original four samples. It's much wider. That means that, you know, there was more variation, which is creating a wider confidence interval, even though the means are fairly close to each other. So the benefit of doing that bootstrapping method is that because we have more samples, we're able to narrow our confidence interval a little bit and therefore have a little bit more confidence in our statistical inference.