It is not true that the higher the confidence level, the narrower the confidence interval. Suppose you have a large population of people and you want to know what their average height is. It’s not practical to measure each and every person, so you take a sample of a hundred people and you measure their height. Let’s say that the average of the sample is 5.8 feet tall, and you want to know how confident you should be about this. So you ask yourself, if I were to repeat this exercise 100 times, what percent of the time would the average of the sample be in a specific range (the range is the confidence interval).

Now let’s think about how the confidence interval is related to the confidence level. Let’s take an example: if the confidence interval were 1 foot to 8 feet, you would know that more than 99 times out of a 100, the sample average would fall in that range, right? However, if you start to narrow the confidence interval to “5 feet to 6 feet”, the confidence level might drop significantly (especially if there are a lot of children in the population). So the confidence level would tend to go down as the confidence interval gets narrower.