1. What is Margin of Error?

The Margin of Error (ME) represents the range of values above and below the sample statistic in a confidence interval. It quantifies the uncertainty in estimating a population parameter from sample data.

2. How Does the Calculator Work?

The calculator uses the Margin of Error formula:

Where:

• \( t \) — Critical value from t-distribution (based on confidence level)
• \( s \) — Sample standard deviation
• \( n \) — Sample size

Explanation: The formula shows that margin of error decreases with larger sample sizes and increases with greater variability in the data.

3. Importance of Margin of Error

Details: Margin of Error is crucial for understanding the precision of survey results and statistical estimates. It helps determine how much confidence we can have in sample statistics representing the true population parameters.

4. Using the Calculator

Tips: Enter the t-value (based on your desired confidence level), the sample standard deviation, and the sample size. All values must be valid (n > 0).

5. Frequently Asked Questions (FAQ)

Q1: How do I determine the t-value?
A: The t-value depends on your confidence level and degrees of freedom (n-1). Common values: 1.96 for 95% CI with large samples.

Q2: What's a good margin of error?
A: Typically 5% or less is acceptable for most surveys, but depends on the context and required precision.

Q3: How does sample size affect ME?
A: ME decreases with the square root of sample size - to halve ME, you need to quadruple sample size.

Q4: When should I use z-score instead of t?
A: Use z-score when population standard deviation is known and sample size is large (typically n > 30).

Q5: Can ME be zero?
A: Only with a census (entire population sampled) or if there's no variability in the data (s=0).