1. What is a Confidence Interval for Proportion?

A confidence interval for a proportion gives an estimated range of values which is likely to include an unknown population proportion. The width of the confidence interval gives us some idea about how uncertain we are about the unknown parameter.

2. How Does the Calculator Work?

The calculator uses the standard confidence interval formula for proportions:

Where:

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

Explanation: The interval is centered around the sample proportion with a margin of error that depends on the confidence level and sample size.

3. Importance of Confidence Intervals

Details: Confidence intervals provide more information than point estimates alone. They indicate the precision of the estimate and allow for better decision making in research and data analysis.

4. Using the Calculator

Tips: Enter the sample proportion (between 0 and 1), sample size (must be positive integer), and select confidence level (90%, 95%, or 99%).

5. Frequently Asked Questions (FAQ)

Q1: What sample size is needed for accurate results?
A: Larger samples give narrower intervals. As a rule of thumb, both n×p and n×(1-p) should be ≥10.

Q2: Why does 95% confidence level give wider intervals?
A: Higher confidence requires wider intervals to be more certain of capturing the true parameter.

Q3: Can I use this for small sample sizes?
A: For small samples or extreme proportions (near 0 or 1), exact methods like Clopper-Pearson may be better.

Q4: What if my proportion is 0 or 1?
A: The formula breaks down at these extremes. Consider Wilson or Jeffreys interval methods instead.

Q5: How is this different from mean CI?
A: Proportion CIs account for the binomial nature of proportion data, while mean CIs assume normal distribution.