1. What is a Confidence Interval for Proportion?

A confidence interval for a population proportion gives an estimated range of values which is likely to include the true population proportion. The width of the interval gives us an idea about the uncertainty of our estimate.

2. How Does the Calculator Work?

The calculator uses the standard confidence interval formula for proportions:

Where:

• \( \hat{p} \) — Sample proportion (observed proportion)
• \( n \) — Sample size
• \( z \) — Z-score corresponding to the desired confidence level

Explanation: The formula accounts for sampling variability, with the margin of error increasing with higher confidence levels and decreasing with larger sample sizes.

3. Importance of Confidence Intervals

Details: Confidence intervals provide more information than point estimates alone by indicating the precision of the estimate and the range of plausible values for the population parameter.

4. Using the Calculator

Tips: Enter the sample proportion (between 0 and 1), sample size (positive integer), and select a confidence level or enter a custom z-score. The calculator will provide the confidence interval and margin of error.

5. Frequently Asked Questions (FAQ)

Q1: What confidence level should I use?
A: 95% is most common, but 90% or 99% may be appropriate depending on your needs for precision versus certainty.

Q2: What if my sample proportion is 0 or 1?
A: The formula breaks down at extremes. Consider using exact methods like the Clopper-Pearson interval in these cases.

Q3: How large should my sample size be?
A: Larger samples yield narrower intervals. A common rule is that both n*p and n*(1-p) should be ≥10.

Q4: When is this formula not appropriate?
A: For very small samples or proportions near 0 or 1, alternative methods like Wilson score interval may be better.

Q5: What does the margin of error represent?
A: It's half the width of the confidence interval, representing the maximum expected difference between sample and population proportions.