Confidence Intervals — Complete SAT Math Guide
🎯 What You'll Master
Confidence intervals appear on the SAT in the Problem Solving & Data Analysis domain. This lesson covers everything you need: definitions, interpretation, comparing intervals, evaluating claims, and sample size calculations — with 7 fully worked examples and practice problems.
1. What Is a Confidence Interval?
A confidence interval (CI) is a range of values calculated from sample data that likely contains the true population parameter.
It is written as: (lower bound, upper bound)
This means: We are 95% confident the true population average height falls within this range.
Think of it as casting a net: the confidence interval is the net, and the true population value is the fish we're trying to catch.
2. What Confidence Level Means
A 95% confidence level means:
If we repeated the sampling process many times, approximately 95% of the resulting intervals would contain the true population value.
❌ INCORRECT Interpretation
"There is a 95% probability the true value is in this specific interval."
The true value is fixed — it either IS or IS NOT in the interval. There's no probability about it for a specific interval.
✅ CORRECT Interpretation
"We are 95% confident the true population parameter falls between the lower and upper bounds."
The confidence is about the method, not about any single interval.