Confidence Intervals: Proportions
Estimate a population proportion.
Key idea
Estimate a population proportion.
In depth
p̂ ± z*√(p̂(1 − p̂)/n) estimates a true proportion. It needs enough successes and failures (at least about 10 each) for the normal approximation.
Worked example
520 of 1,000 support: p̂ = 0.52, SE ≈ 0.0158, 95% CI ≈ 0.52 ± 0.031.
Formula
Real-world uses
- Reporting that between 42% and 48% of voters support a policy in a poll
Common mistake
Using it when counts are very small.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Confidence Intervals: Proportions?
Estimate a population proportion. It is a topic at the expert level in Probability & Statistics.
What is the formula for Confidence Intervals: Proportions?
The key formula is p̂ ± z√(p̂(1−p̂)/n).
Where is Confidence Intervals: Proportions used in real life?
Real-world examples: Reporting that between 42% and 48% of voters support a policy in a poll.
What should I learn before Confidence Intervals: Proportions?
Make sure you are comfortable with Confidence Intervals for Means, the previous topic in Probability & Statistics.
What is a common mistake with Confidence Intervals: Proportions?
Using it when counts are very small.
How can I practise Confidence Intervals: Proportions?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Confidence Intervals: Proportions?
Move on to Hypothesis Testing Basics next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.