What is a Confidence Interval?
A confidence interval is a range of values, derived from sample data, that is likely to contain the true value of an unknown population parameter. In simple terms, it provides an estimated range for an unknown population mean, proportion, or other statistical measure, rather than a single point estimate.
Key Principles of Confidence Intervals
The interval is always accompanied by a 'confidence level,' typically expressed as a percentage (e.g., 90%, 95%, 99%). This level indicates the long-run probability that if the same sampling method were repeated many times, the calculated interval would contain the true population parameter. It does not mean there's a 95% chance the true value falls within *this specific* interval.
A Practical Example
Imagine a survey finds that 60% of voters support a new policy. A 95% confidence interval for this poll might be [57%, 63%]. This means that if the survey were conducted many times, 95% of the resulting confidence intervals would contain the true percentage of voters who support the policy. The interval helps understand the precision of the estimate.
Importance and Applications
Confidence intervals are crucial in research, quality control, and public opinion polling because they quantify the uncertainty of an estimate. They allow researchers to communicate the reliability of their findings beyond a single point value, making it clear that a sample estimate is only an approximation of the larger population.