core practice · coding problem
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.)
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].
Try this drill in the practice workspace →
Hints when you need them
- SE = √(p̂(1−p̂)/n).
- CI = p̂ ± z·SE.
Watch for these mistakes
- Saying 'there is a 95% chance the true value is in this interval'
- Using the normal approximation with tiny samples
- Ignoring that CI width grows with desired confidence level