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Margin Of Error Formula:
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The Margin Of Error (ME) quantifies the uncertainty in a point estimate from sample data. It represents the range within which the true population parameter is expected to lie with a certain level of confidence.
The calculator uses the Margin Of Error formula:
Where:
Explanation: The formula calculates the range of values around the point estimate that likely contains the true population parameter, based on the sample statistics and chosen confidence level.
Details: Calculating margin of error is essential for understanding the precision of statistical estimates, interpreting survey results, and making informed decisions based on sample data with known confidence intervals.
Tips: Enter the z-score corresponding to your desired confidence level (e.g., 1.96 for 95% confidence), the population standard deviation, and the sample size. All values must be valid (n > 0, σ ≥ 0).
Q1: What is a z-score and how do I find it?
A: A z-score represents the number of standard deviations from the mean. Common values: 1.645 (90% confidence), 1.96 (95% confidence), 2.576 (99% confidence).
Q2: When should I use this margin of error formula?
A: Use this formula when you know the population standard deviation and are working with a normally distributed population or large sample sizes (n ≥ 30).
Q3: What if I don't know the population standard deviation?
A: When population standard deviation is unknown, use the t-distribution with sample standard deviation instead of the z-distribution.
Q4: How does sample size affect margin of error?
A: Margin of error decreases as sample size increases. Larger samples provide more precise estimates with smaller margins of error.
Q5: Can margin of error be negative?
A: No, margin of error is always a positive value representing the range above and below the point estimate.