University of Minnesota, Twin Cities School of Statistics Stat 3011 Rweb Textbook (Wild and Seber)
Example 1.1.3 discusses the variability of "estimates" derived from random samples. Different random samples result in different estimates. In this example, the population size is N = 5700. Random samples of several different sizes are compared. In Figure 1.1.1 samples of size n = 20 are compared with samples of size n = 500.
Below is an Rweb form that allows you to do one of these simulations. Click "Submit" to see the results. The results are different every time you do it because the computer creates different random samples every time. But each time it should look more or less like the top panel in Figure 1.1.1 in Wild and Seber. The center of the pattern of dots should be near the dotted line indicating the true population proportion and the spread of the pattern of dots should be about the same as in the figure in the text.
n <- 500and you should get something more or less like the bottom panel in Figure 1.1.1.
As for how the rest of the simulation works, you are not expected to understand this yet. If you look under the hood of a car, it is very complicated, but you don't have to understand everything about how it works in order to drive the car. The way Rweb works exposes whats "under the hood" because all of the code for a simulation must appear in the submitted form. You are not responsible for understanding the nuts and bolts of complicated simulations like this, only the big picture.
It will be clear what computing you are responsible for understanding the details of. If it's on homework, you're responsible. If not, not.
So just relax here and look at the pictures. We'll worry about computing later.
Below is an even more complicated simulation that allows us to compare several different sample sizes on one plot.