A confidence interval, as described by W3Schools, is defined by a lower bound and an upper bound. This construct provides a specific range of values within which the true parameter being estimated is likely to fall.
Understanding Confidence Intervals
When we calculate a confidence interval, we are essentially creating an estimated range for an unknown population parameter, such as a mean or a proportion. Instead of providing a single point estimate, which might not be exact, a confidence interval offers a more robust estimation by giving an interval.
Key Components
- Lower Bound: This is the smallest value in the range.
- Upper Bound: This is the largest value in the range.
- Range of Values: The span between the lower and upper bounds, representing where the true population parameter is expected to lie.
Practical Example
To illustrate, consider an example provided by W3Schools:
- Scenario: Estimating the average height of people in Denmark.
- Confidence Interval: It might be stated that "The average height of people in Denmark is between 170 cm and 190 cm."
In this example, 170 cm would be the lower bound and 190 cm would be the upper bound. This indicates that based on the statistical analysis, the true average height of the Danish population is likely to be within this 20 cm range.
Why Use Confidence Intervals?
Confidence intervals are crucial in statistics because they:
- Provide a measure of the precision or uncertainty of an estimate. A narrower interval suggests a more precise estimate.
- Offer a more informative result than a single point estimate alone.
- Are widely used in research, polls, and quality control to quantify the reliability of findings.
