Students often struggle with the idea of statistical power. The left panel shows the rejection region and how it changes with the size of the test, the population variance and the extremity of the alternative hypothesis. The right panel shows the power curve and how it scales with the same inputs. Additionally, I've found that animating these inputs (especially the alternative hypothesis) helps students better understand these concepts.

In my class, I stressed what a confidence interval is and what it is not. This app Matt Butner and I developed shows that we can't assume any single confidence interval "contains the true mean," rather 95% of confidence intervals constructed in the same way contain the true mean. I also stress how confidence intervals shrink when you increase the sample size or decrease the confidence level.