Margin of Error and Confidence Intervals
A confidence interval is the mean of your estimate plus and minus the margin of error. This is the range of values you expect your estimate to fall between if you redo your test, within a certain level of confidence. Confidence, in statistics, is another way to describe probability.
Confidence intervals are most often constructed using confidence levels of 95% or 99%.
Calculating Confidence Intervals
Suppose a group of researchers is studying the heights of high school basketball players. The researchers take a random sample from the population and establish a mean height of 74 inches.
The mean of 74 inches is a point estimate of the population mean. A point estimate by itself is of limited usefulness because it does not reveal the uncertainty associated with the estimate; you do not have a good sense of how far away this 74-inch sample mean might be from the population mean.
At a 95% confidence level, researchers calculate a margin of error of ±2, plus and minus 2.
Add and subtract 2 from the sample mean, 74, to get the confidence interval: (72, 76)
We are 95% confident the true mean of all high school basketball player heights is between 72 and 76 inches.