Track 7 · Estimation and Confidence Intervals · Lesson 2 of 10
The idea of an interval estimate
Build an interval estimate as estimate ± margin of error and explain what makes the interval wider or narrower.
A news site reports that 42% of residents support a new tram line. Is the real figure probably 41%? Could it be 50%? A single number cannot say. An interval — “42%, give or take 3 points” — tells readers how far the estimate can be trusted.
A point estimate is almost never exactly right: a different sample would give a different number. An interval estimate gives a range of plausible values for the parameter, built so that the method rarely misses.
Nearly every interval in this track has the same shape: a point estimate plus and minus a margin of error.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Build an interval as estimate ± critical value × standard error
- Recover the estimate and the margin from a reported interval
- Explain how the confidence level, variability and sample size change the width
- State what a margin of error does and does not cover