Statistical Definitions

Now, for some important statistical definitions related to sampling, let’s take another look at our 1,000 repeated/replicated virtual samples of size $𝑛$= 25, $𝑛$= 50, and $𝑛$= 100.

These types of distributions have a special name, which is sampling distributions. Their visualization displays the effect of sampling variation on the distribution of any point estimate, in this case, the sample proportion $\hat{p}$. Using these sampling distributions for a given sample size $n$, we can make statements about what values we can typically expect.

For example, observe the centers of all three sampling distributions—they’re all roughly centered around 0.4 = 40%. Furthermore, observe that while we’re somewhat likely to observe sample proportions of red balls of 0.2 = 20% when using the shovel with 25 slots, we’ll almost never observe a proportion of 20% when using the shovel with 100 slots. Observe also the effect of sample size on the sampling variation. As the sample size$𝑛$ ...