Data Analytics: Foundations to Practice · Statistical Inference Basics
Confidence Intervals
A confidence interval communicates a range and a confidence level together, and both pieces of information are necessary; reporting a single point estimate alone implies a false precision the underlying sample simply cannot support.
A confidence interval provides a range of plausible values for a population characteristic, along with a stated confidence level, such as reporting that average customer satisfaction is estimated at 7.2 out of 10, with a 95 percent confidence interval of 6.9 to 7.5; this range acknowledges honestly that the true population value is very unlikely to be exactly the single point estimate calculated from the specific sample actually collected.
Key Takeaways
- A confidence interval provides a range of plausible values plus a stated confidence level, acknowledging the true population value likely isn't exactly the point estimate.
- A 95% confidence level means 95% of intervals from repeated sampling would contain the true value, not a 95% probability for this one specific interval.
- Interval width is influenced by sample size, underlying data variability, and the chosen confidence level itself.
- Reporting only a point estimate without an interval implies false precision that a sample-based estimate genuinely cannot support.