Confidence intervals (CIs) are used to estimate the range within which a population parameter (e.g., a mean or proportion) is likely to fall, based on sample data. The interval provides a measure of uncertainty or precision around the sample estimate.

The key purposes are:

1. Estimate Population Parameters: CIs give a range for the true value of the parameter.
2. Account for Sampling Variability: They reflect how much the estimate might vary from sample to sample.
3. Provide More Information than Point Estimates: Unlike a single estimate (e.g., the sample mean), CIs indicate the reliability of that estimate.

For example, saying “the average body weight of the basket ball team is 83 kg, with a 95% confidence interval of [73kg, 93kg]” means we are 95% confident that the true average weight of all basketball players lies within that range.

How to Interpret Confidence Intervals

1. In Plain Terms:
   A 95% confidence interval means that if you repeated the experiment or sampling many times, 95% of the intervals calculated would contain the true population parameter.
2. Key Points to Remember:
   • The interval is about the parameter, not the data or sample.
   • A wider interval indicates more uncertainty, often due to a small sample size or high variability.
   • A narrower interval suggests higher precision in the estimate.
3. What It Does Not Mean:
   • It does not mean there is a 95% probability the true parameter is in the specific interval calculated (the true parameter is fixed; the interval varies).
   • It is not a range for individual data points.