In this simulation experiment we draw 1000 (different) random samples from the hospital dataset. Below you can select the sample size. Vary the sample size and observe what happens with the sampling distribution. The red vertical line represents the population mean.
Here, we now draw 100 random samples of size 50 (of the hospital dataset) and compute the confidence interval for each of those 100 samples. How many CIs do you think will cover the population mean? Play around with the significance level and test your understanding.