Math
Confidence intervals for proportions.
Definition
A confidence interval for a proportion gives a range of plausible values for the true population proportion based on sample data. It uses the sample proportion, sample size, and a z-critical value to construct the interval.
How it works · 5 phases
Step by step.
- Calculate the sample proportion p̂ = x/n
- Check conditions: np̂ ≥ 10 and n(1 - p̂) ≥ 10
- Find the critical z-value for your confidence level
- Compute the margin of error: z* · √(p̂(1-p̂)/n)
- The interval is p̂ ± margin of error
Examples
Real-world.
- 1 A poll finds 60% of 500 voters support a measure; the 95% CI is about (0.557, 0.643)
- 2 Estimating the proportion of defective items in a factory shipment
- 3 Determining what fraction of students prefer online classes
Key Fact
CI: p̂ ± z*√(p̂(1-p̂)/n)