1. What is a Sample Size Calculator?

Definition: This calculator determines the required sample size for a statistical survey based on confidence level, expected proportion, and margin of error.

Purpose: It helps researchers and analysts determine how many observations are needed for statistically significant results.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( n \) — Required sample size
• \( Z \) — Z-score (determined by confidence level)
• \( p \) — Expected proportion (decimal between 0 and 1)
• \( e \) — Margin of error (decimal between 0 and 1)

Explanation: The formula calculates the minimum number of samples needed to achieve the desired confidence level and precision.

3. Importance of Sample Size Calculation

Details: Proper sample size ensures study validity, prevents resource waste, and provides statistically meaningful results.

4. Using the Calculator

Tips:

• For 95% confidence, use Z=1.96 (default)
• When unsure of proportion, use p=0.5 (most conservative)
• Common margin of error values are 0.05 (5%) or 0.03 (3%)

5. Frequently Asked Questions (FAQ)

Q1: How do I choose the right Z-score?
A: Z-score corresponds to confidence level: 1.645 (90%), 1.96 (95%), 2.576 (99%).

Q2: Why use 0.5 for proportion?
A: 0.5 gives the maximum sample size, ensuring adequate sampling when true proportion is unknown.

Q3: What's a reasonable margin of error?
A: Typically 3-5% for surveys, but depends on study requirements.

Q4: Does this work for small populations?
A: For populations under 20,000, use finite population correction.

Q5: How does sample size affect study cost?
A: Larger samples increase cost but improve precision - balance is key.