Why does the confidence interval itself get larger as the probability of your being correct increases (from, say, 95% to 99%)? Because the larger range of the confidence interval (in this case, 19.6 [73.8, 54.2] for a 95% confidence interval vs. 25.6 [76.8, 51.2] for a 99% confidence interval) allows you to encompass a larger number of possible outcomes and you can thereby be
