1. What is the Margin of Error for Mean?

The margin of error (MOE) for a mean is a statistic expressing the amount of random sampling error in a survey's results. It represents the radius of the confidence interval for a reported mean and indicates how close the sample mean is likely to be to 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 (higher standard deviation).

3. Importance of Margin of Error

Details: The margin of error is crucial in determining the precision of sample estimates. It helps researchers and analysts understand the reliability of their results and is essential for constructing confidence intervals.

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: What are common z-score values?
A: Common values are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q2: How does sample size affect MOE?
A: MOE decreases as sample size increases, following an inverse square root relationship.

Q3: When is this formula appropriate?
A: When sampling from a normally distributed population or when sample size is large enough (n > 30) for the Central Limit Theorem to apply.

Q4: What if my population is finite?
A: For finite populations, a finite population correction factor should be applied to the formula.

Q5: How is this different from proportion MOE?
A: For proportions, the standard deviation is estimated as √(p(1-p)), while for means we use the actual sample standard deviation.