7.3: Confidence Intervals
An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence interval is represented as - L1, followed by a point estimate such as sample proportion or sample mean, followed by L2. The confidence limits can be calculated as follows :
L1 = point estimate - margin of error, E
L2 = point estimate + margin of error, E
A confidence interval allows a researcher to determine the uncertainty of a point estimate in predicting the true value of a population parameter. In other words, as the confidence interval narrows, the accuracy of the point estimate in predicting the actual value of a population parameter increases.
Further, a confidence level is used to check if a confidence interval contains a population parameter. The common choices for a confidence level are 90%, 95%, and 99%.