CONFIDENCE INTERVAL
Back to GlossaryDefinition
A range of values derived from sample data that likely contains the true population parameter at a stated confidence level.
Summary
A confidence interval is like a 'best guess range' for an unknown population value based on sample data. Think of it as saying 'we're X% confident that the true answer lies somewhere between these two numbers.' For example, if we survey 100 people about their income and calculate a 95% confidence interval of $40,000-$50,000, we're saying we're 95% confident the true average income of the entire population falls within this range. The confidence level (like 95%) tells us how often our method would capture the true value if we repeated the process many times.
Usage Context
Essential for understanding statistical inference, hypothesis testing, interpreting research results, and making decisions with uncertainty. Critical when learning about estimation theory and preparing for advanced topics in experimental design.
Common Confusions
- Thinking the confidence level is the probability that the true parameter is in a specific interval
- Confusing confidence intervals with prediction intervals
- Believing a wider interval means less accuracy (when it actually means more confidence)
- Thinking you need the population to be normally distributed (when it's the sampling distribution that matters)
- Confusing the confidence level with the significance level in hypothesis testing
