1. What is Margin of Error for Mean?

The Margin of Error (MOE) quantifies the amount of random sampling error in a survey's results. It represents the radius of the confidence interval for a reported statistic, indicating how much the sample mean may differ from the true population mean.

2. How Does the Calculator Work?

The calculator uses the Margin of Error formula:

Where:

• \( z \) — Z-score corresponding to the desired confidence level
• \( SD \) — Standard deviation of the sample
• \( n \) — Sample size

Explanation: The formula shows that margin of error decreases as sample size increases, 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 making informed decisions based on statistical data. It helps determine how much confidence we can have in sample estimates.

4. Using the Calculator

Tips: Enter the z-score corresponding to your desired confidence level (e.g., 1.96 for 95% confidence), the sample standard deviation, and the sample size. All values must be valid (n > 0).

5. Frequently Asked Questions (FAQ)

Q1: How do I choose the right z-score?
A: Common z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence). These come from the standard normal distribution.

Q2: What's the relationship between sample size and margin of error?
A: MOE decreases as sample size increases, but the relationship isn't linear - doubling the sample size reduces MOE by about 30%.

Q3: When should I use this formula?
A: Use it when you have a random sample and want to estimate the precision of your sample mean. It assumes the sampling distribution is normal or nearly normal.

Q4: What if my population is small?
A: For populations less than 20 times the sample size, consider using a finite population correction factor.

Q5: Can I use this for proportions?
A: No, proportions use a different MOE formula: \( MOE = z \times \sqrt{(p(1-p)/n)} \).