The interpretation of a confidence interval has the basic template of: "We are 'some level of percent confident' that the 'population of interest' is from 'lower bound to upper bound'. After Ellie calculates at 95% confidence interval, she could say she is 95% confident that the true population average number of miles run by marathon runners is between “the values of the confidence interval”. The phrases in single quotes are replaced with the specific language of the problem. We will discuss more about the interpretation of a confidence interval after we provide a few more examples.
Some might say, "Why not just be 100% confident?", but that does not make practical sense. For instance, what value comes from me saying I am 100% confident that the approval rating for the President is from 0% to 100%. That is the only interval in which one can be truly confident will capture the actual proportion. Similarly, if you were to ask your professor what they think your score will be on an exam and they reply, "zero to one hundred", what would you think of that answer?
However, one does want to be as confident as reasonably possible. Most confidence levels use ranges from 90% confidence to 99% confidence, with 95% being the most widely used. In fact, when you read a report that includes a margin of error, you can usually assume this has a 95% confidence attached to it unless otherwise stated.
We're going to begin exploring confidence intervals for one population proportions. The important issue of determining the required sample size to estimate a population proportion will also be discussed in detail in this lesson.