1. What is Sample Proportion?

The sample proportion (p̂) is a statistic that estimates the proportion of successes in a population based on a sample. It is calculated as the number of successes divided by the sample size.

2. How Does the Calculator Work?

The calculator uses the sample proportion formula:

Where:

• \( x \) — Number of successes in the sample
• \( n \) — Total sample size
• \( \hat{p} \) — Sample proportion (unitless)

Explanation: The formula gives the proportion of items with a particular characteristic in a sample, which serves as an estimate for the population proportion.

3. Importance of Sample Proportion

Details: Sample proportion is fundamental in statistics for estimating population parameters, constructing confidence intervals, and performing hypothesis tests about proportions.

4. Using the Calculator

Tips: Enter the number of successes (x) and sample size (n). Both must be non-negative integers with x ≤ n. The result is a proportion between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between p and p̂?
A: p represents the true population proportion, while p̂ is the sample estimate of that proportion.

Q2: How large should my sample be?
A: For reliable estimates, n should be large enough that both np̂ and n(1-p̂) are ≥10 for normal approximation.

Q3: Can p̂ be 0 or 1?
A: Yes, but these extreme values may require special statistical methods for inference.

Q4: How accurate is p̂ as an estimate?
A: Accuracy depends on sample size and sampling method. Larger random samples give more precise estimates.

Q5: What's the standard error of p̂?
A: Standard error = √[p̂(1-p̂)/n], which measures the variability of the estimate.