1. What is Standard Error for Population Proportion?

The standard error (SE) of a population proportion measures the variability in the sampling distribution of the sample proportion. It quantifies how much the sample proportion is expected to fluctuate from the true population proportion.

2. How Does the Calculator Work?

The calculator uses the Central Limit Theorem formula for population proportion:

Where:

• \( p \) — Population proportion (between 0 and 1)
• \( n \) — Sample size (≥1)

Explanation: The formula shows that standard error decreases as sample size increases, and is maximized when p = 0.5.

3. Importance of Standard Error Calculation

Details: The standard error is crucial for constructing confidence intervals and conducting hypothesis tests about population proportions.

4. Using the Calculator

Tips: Enter the population proportion (between 0 and 1) and sample size (≥1). The calculator will compute the standard error of the sampling distribution.

5. Frequently Asked Questions (FAQ)

Q1: When is this formula valid?
A: The formula works when the sample size is large enough (typically np ≥ 10 and n(1-p) ≥ 10) for the Central Limit Theorem to apply.

Q2: What does a smaller standard error indicate?
A: A smaller SE suggests the sample proportion is likely to be closer to the true population proportion.

Q3: How is this related to confidence intervals?
A: A 95% confidence interval for p would be sample proportion ± 1.96 × SE.

Q4: Why does standard error decrease with larger n?
A: Larger samples provide more information about the population, reducing sampling variability.

Q5: What if p is unknown?
A: Use the sample proportion or the conservative estimate p = 0.5 (which maximizes the standard error).