Understanding Confidence Intervals
A confidence interval gives us a range of plausible values for an unknown population parameter. The confidence level (e.g., 95%) tells us how often the interval would contain the true parameter if we repeated the sampling process many times.
Key Points:
- The confidence level is NOT the probability that the parameter lies within a specific interval
- It's the long-run proportion of intervals that contain the true parameter
- Wider intervals → higher confidence; Narrower intervals → lower confidence
- Larger sample sizes → narrower intervals (more precision)
Green intervals contain the true mean
Red intervals do not contain the true mean