What is the difference between confidence level and confidence interval?

Answer 1

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Confidence level is a percentage, typically 95% or 99%. It is how confident you are that the true mean, proportion, or other statistic for which you are trying measure is between the two endpoints in the confidence interval. The numbers in the confidence interval are of the same units as the statistic you are trying to locate.

For example, let's say you are trying to determine the mean age of Camaro drivers. Then you take a random sample, calculate the sample mean, then use that as the point estimate for the true population mean (which is unknown). You can construct many different confidence intervals from your gathered information. Let's say that you ended up sampling 50 drivers, and their mean age was 26. Then you decided to calculate some confidence intervals.

(I'll make up some numbers for the sake of this example)

The 95% confidence interval might be something like [24, 28]. In other words, you are 95% confident that the true mean age of Camaro drivers is between 24 and 28.

The 99% confidence interval might be something like [22, 30]. In other words, you are 99% confident that the true mean age of Camaro drivers is between 22 and 30.

The higher the level of confidence, the wider the interval. The lower the level of confidence, the shorter the interval. It's a trade off. Ideally, you would like to pinpoint the true value, that is, you would like to have a very short confidence interval, but you would also like to be very confident. This can be a difficult task. This is why the size of the sample becomes important. The larger the sample size, the smaller the standard error and the smaller the interval.