# Construct a 95% confidence interval

> n = 100 coin flips, 55 heads. Assuming a normal approximation, construct a 95% CI for the true heads probability p. (Use z = 1.96.)

Canonical: https://learn.significanthobbies.com/curriculum/drills/construct-confidence-interval

n = 100 coin flips, 55 heads. Assuming a normal approximation, construct a 95% CI for the true heads probability p. (Use z = 1.96.)

## The mechanism

A confidence interval is a procedure, not a probability statement about one interval. If you repeated the experiment many times, 95% of the intervals you'd construct would contain the true parameter. Wider interval = more uncertainty or less data.

## Expected evidence

p̂ = 0.55, SE ≈ 0.0498, CI ≈ [0.452, 0.648].

## Hints

- SE = √(p̂(1−p̂)/n).
- CI = p̂ ± z·SE.

## Sources and practice

- [MIT 18.650 Statistics for Applications](https://ocw.mit.edu/courses/mathematics/18-650-statistics-for-applications-fall-2016/)
- [Study Estimation & Confidence Intervals](https://learn.significanthobbies.com/curriculum/concepts/estimation-confidence)
- [Try the interactive drill](https://learn.significanthobbies.com/drills/construct-confidence-interval)
- [All practice briefs](https://learn.significanthobbies.com/curriculum/drills/)