1. What is Sample Proportion Distribution?

The sample proportion distribution describes the probability distribution of sample proportions from repeated random sampling. It follows a normal distribution when sample size is sufficiently large, with mean equal to the population proportion and standard deviation calculated using the formula.

2. How Does the Calculator Work?

The calculator uses the sample proportion distribution formula:

Where:

• \( p \) — Population proportion (0 to 1)
• \( n \) — Sample size (count)
• \( \mu \) — Mean of the sampling distribution
• \( \sigma \) — Standard deviation of the sampling distribution

Explanation: The formula calculates the center and spread of sample proportions when repeatedly sampling from a population with proportion p.

3. Importance of Sample Proportion Distribution

Details: Understanding the sampling distribution of proportions is crucial for statistical inference, hypothesis testing, and constructing confidence intervals for population proportions.

4. Using the Calculator

Tips: Enter population proportion (between 0 and 1) and sample size (positive integer). The calculator will compute the mean and standard deviation of the sampling distribution.

5. Frequently Asked Questions (FAQ)

Q1: When is the normal approximation appropriate?
A: The normal approximation works well when both np ≥ 10 and n(1-p) ≥ 10.

Q2: What if my sample size is small?
A: For small samples or extreme proportions, the binomial distribution should be used instead of the normal approximation.

Q3: How is this used in confidence intervals?
A: The standard deviation (σ) is used to calculate the margin of error for proportion confidence intervals.

Q4: Can I use this for hypothesis testing?
A: Yes, this distribution forms the basis for z-tests about population proportions.

Q5: What are common applications?
A: This is widely used in survey analysis, quality control, medical studies, and political polling.