STATISTICS

THE ART & SCIENCE OF LEARNING FROM DATA

AGRESTI · FRANKLIN · KLINGENBERG

### You can use one of the options to the left to vary the binsize of the histogram, or to zoom into it, i.e. adjust the range of the x-axis. You should also ask your students if this distribution looks normal, and hopefully they will pick up the slight left skew of this sampling distribution. (One option on the left allows you to overlay a normal distribution.)

### You can now demonstrate what happens if the sample size gets larger. Let's increase it to 10. Just click on the arrow up in the "Select sample size (n)" box once to get to a sample size of 10. The histogram of the sampling distribution will update with a fresh set of 10,000 generations of samples of size 10:

### However, taking a sample of, say, n=3000 flights results in a normal sampling distribution:

### The sample mean of 67.3 is indicated with a blue triangle, and one sees that it falls a bit below the population mean of 71.7, indicated with an orange half circle. These two values are also shown in the bottom plot, which will keep track of all sample means generated. To see this in action, click on the Draw Sample(s) button a few more times and point out to your students how the sample mean varies around the population mean, for a nice visualization of sampling variability. After you get tired of clicking, opt to generate 10,000 samples (of size 5) at once, and you should get a nice visualization of the sampling distribution:

### This is a good example to tell your students that in statistics, sometimes "large" (or infinity) means n=35, but sometimes n=3000. If you have an interesting population distribution that you want to be implemented, please let me know!

__Flight arrival delays__

### For the preloaded population distribution about the delay (in min.) of all flights arriving at Atlanta airport in January of 2017, a sample size of 35 will not result in a bell-shaped sampling distribution because the population distribution is so skewed. (Note that I needed to zoom into the x-axis for the sampling distribution to see it more clearly. This is not shown in the screenshot.)

### You can mention that with a sample size of 10 the sample means tend to fall closer to the population mean, by pointing out the smaller range of the sampling distribution when n=10. This is nice to show using the app by just toggling between a sample size of 5 and 10 by pressing the arrow up and arrow down button in "Select sample size (n)". Finally, increase the sample size to n=35, say, and point out that it now looks fairly normal: