Imagine that you've just enrolled at Crammer Nation University and finished your first day of classes. You just called it quits on your high school relationship, and are looking to hop right into the college action.
It's fraternity rush season, and you hear that the brothers of Sigma Apple Pi absolutely pull. For the sake of this example, let's say that the average Tinder matches per day that brothers of Sigma Apple Pi get is unknown, but you've heard it's high.
You decide to test things out by taking a sample of Sigma Apple Pi brothers to establish a range of values in which you can be confident the true population mean for brothers' Tinder matches per day lies.
Herein lies the purpose of a confidence interval...
A confidence interval enables one to obtain a range of values in which the true population parameter lies, with a defined confidence level.
Confidence intervals explained
Without digging into the math yet, let's say you surveyed 35 random brothers and found that the sample had a mean of 23.2 Tinder matches per day with a standard deviation of 3.2 matches. Based on these numbers, we can compute the following 95% confidence interval (CI):
This means we're 95% confident that the true mean Tinder matches per day for brothers of Sigma Apple Pie lies within this interval for the entire population of brothers. We are not saying that there's a 95% probability... rather that we are 95% confident. (Click here to skip ahead and understand what this means.)