## Question 735:

1

No answer provided yet.In learning statistics, we learn that much of what we do involves making decisions from samples of data, rather than from the entire set or population. When we deal with a sample there will always be uncertainty. For this reason, we can never be 100% sure of our decisions based on data. We can however quantify our certainty and confidence intervals are a great way to do that. Confidence intervals provide a likely range that the unknown parameter we're measuring will likely fall-within. For example, if we're interested in the average height of all 8th grade boys in a school district, we could sample say 100 of them from several schools then take the average. This average would be an estimate around the unknown average of ALL 8th grade boys in the district. The chance that is exactly the same is remote, so we provide a likely range or interval the population mean will take. This is the confidence interval. It provides an estimate of both location (the average height) and uncertainty--the smaller the sample the wider our confidence interval will be around the mean--thus showing how much uncertainty there is in our estimate.

In the real world, confidence intervals can be extremely helpful in for example in estimating salaries for a given profession. If you wanted to know the average starting salary of an attorney, you could sample several attorney's salaries (hoping they tell you the truth of course) then compute the mean and confidence interval around the mean. This confidence interval could tell you the likely range for the average starting salary and can help students in college who are contemplating law school--but aren't sure if the expense of law school would be worth it in the first few years after graduation.