and this really mirrors what we think the sampling distribution would look like of course we couldn't do 4,000 real random samples from the population we only have one random sample but this kind of simulates what the sampling distribution would look like if we had 4,000 random samples from the population there is a very big difference the middle is the big difference in an in a in a real sampling distribution we need to take random samples from the population the middle is the population but when you do a bootstrap you're taking samples from the original sample so the middle is actually just going to be the sample statistic or not in this case 98 point 2 6 you can see how the the center of the distribution is really close to ninety eight point two six but in terms of standard error and shape it mirrors what we think the sampling distribution would look like so again we want to make a 95% confidence interval this does not have to match up with a normal T curve though it does actually it matches up very nice since it looks very normal so we'll go to to tail and we were you doing 95 percent so we'll leave this as 95 percent here and if you notice the numbers here's the lower limit ninety-eight point zero five three and ninety-eight point four eight now in a bootstrap you will get slight variations in these numbers because your random samples are not the same as my random sample so every time you do this you will get something just slightly different okay so with this bootstrap I'm 95% confident that the population mean average body temperature is somewhere between 98 point zero five three degrees Fahrenheit and ninety-eight point four eight zero degrees Fahrenheit all right so that's bootstrapping and stat kado so stat kado is the traditional normal formulas stack key we're doing the bootstrap which is again calculating the confidence interval directly from the bootstrap distribution without formulas now the interesting thing that you can do with this also is you can actually bootstrap median like if you want to find a population median confidence interval you can change this to median so I can kind of do a 95% confidence interval for the median median would be in between these two numbers I can also click on standard deviation these are all things that are kind of difficult to deal with with formulas especially median if this tests of not look very nice with the sampling distribution so the the standard deviation for the population standard deviation for body temperature is somewhere between 0.5 72 and 0.95 3 or 95% confident that is so there's some interesting things you can do with this bootstrap as well all right all right well thanks for spending some time with me and this is Matt to show and intro stats and I will see you next time