A confidence interval is how much **uncertainty** there is with any particular **statistic**. Confidence intervals are often used with a **margin of error**. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to **survey the entire population**. Confidence intervals are intrinsically connected to **confidence levels**.

## Confidence Intervals vs. Confidence Levels

Confidence levels are expressed as a percentage (for example, a 95% confidence level). It means that should you repeat an experiment or survey over and over again, 95 percent of the time your results will match the results you get from a population (in other words, your statistics would be sound!). Confidence intervals are your results and they are usually numbers. For example, you survey a group of pet owners to see how many cans of dog food they purchase a year. You test your statistics at the 99 percent confidence level and get a confidence interval of (200,300). That means you think they buy between 200 and 300 cans a year. You’re super confident (99% is a very high level!) that your results are sound, statistically.

## How to Interpret Confidence Intervals

Suppose that a 90% confidence interval states that the population mean is greater than 100 and less than 200. How would you interpret this statement?

Some people think this means there is a 90% chance that the population mean falls between 100 and 200. This is incorrect. Like any population parameter, the population mean is a constant, not a random variable. It does not change. The probability that a constant falls within any given range is always 0.00 or 1.00.

The confidence level describes the uncertainty associated with a *sampling method*. Suppose we used the same sampling method to select different samples and to compute a different interval estimate for each sample. Some interval estimates would include the true population parameter and some would not. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter; a 95% confidence level means that 95% of the intervals would include the parameter; and so on.

## Confidence Interval Data Requirements

To express a confidence interval, you need three pieces of information.

- Confidence level
- Statistic
- Margin of error

Given these inputs, the range of the confidence interval is defined by the *sample statistic* __+__ *margin of error*. And the uncertainty associated with the confidence interval is specified by the confidence level.

Often, the margin of error is not given; you must calculate it.

There are four steps to constructing a confidence interval.

- Identify a sample statistic. Choose the statistic (e.g, sample mean, sample proportion) that you will use to estimate a population parameter.
- Select a confidence level. As we noted in the previous section, the confidence level describes the uncertainty of a sampling method. Often, researchers choose 90%, 95%, or 99% confidence levels; but any percentage can be used.
- Find the margin of error. If you are working on a homework problem or a test question, the margin of error may be given. Often, however, you will need to compute the margin of error, based on one of the following equations.
Margin of error = Critical value * Standard deviation of statistic

Margin of error = Critical value * Standard error of statistic

For guidance, see how to compute the margin of error. - Specify the confidence interval. The uncertainty is denoted by the confidence level. And the range of the confidence interval is defined by the following equation.
Confidence interval = sample statistic

__+__Margin of error

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