# Level of Confidence

The level of confidence for a confidence interval estimate indicates what the probability is that the parameter in question is within that range. As the probability grows, the range gets larger.

Let's say I drive a Subaru Forester. Let's say its reported miles per gallon in highway driving is 24 mpg. So that is our estimated mean. Remember it's just an estimate.

So now let's say we take 100 observations of my driving trips on the highway as our sample set. I get all sorts of numbers for my trips based on the weather and my mood and traffic and so on. They're all sort of around 24 mpg but not exactly that number.

So we might say that our range is 18 - 30 mpg and that we are 99% confident that this includes the mean. It's really, really likely, but there is always the outlier chance that the mean isn't in that range. The 99% "high" number (out of 100) matches with a wide range.

Now say we narrow the range to 22 - 26 mpg. At this point we are let's say 88% confident that we include the mean. The range is narrower. There's more chance of missing.

Next let's say we narrow the range to 23.5 to 24.5 mpg. The range is really tiny. We might only be 30% confident at this point. It's fairly likely that our actual population mean is not in this very narrow range. It could be - but it's not an even proposition.

Again this estimate is all about this particular sample set. We might take a fresh sample set with 500 observations and our confidence interval and confidence levels will all be different based on that new sample.

Statistics Basics