gen-briefly-explain-a-confidence-interval-and-one-common-misconc-2a55

Briefly explain a confidence interval and one common misconception about it.

# Confidence Interval A **confidence interval** is a range of values calculated from sample data that likely contains an unknown population parameter. For example, a 95% confidence interval for average height might be 165-175 cm, meaning we're "95% confident" the true population average falls within this range. ## Common Misconception **The misconception:** "There's a 95% probability that the true parameter lies within this specific interval." **The reality:** Once calculated, a specific confidence interval either contains the true parameter or it doesn't (probability = 0 or 1). The 95% refers to the *method*—if we repeated our sampling process many times, about 95% of the intervals we'd construct would capture the true parameter. It's about the long-run reliability of the procedure, not the probability for any single interval. Think of it like a fishing net: a "95% confidence net" will successfully catch the fish 95% of the time you cast it, but once you've cast it, the fish is either in the net or it isn't.