Margin of Error

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What is the Margin of Error (MOE)?

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The Margin of Error (MOE) is a statistic that expresses the amount of random sampling error in a survey's results. It indicates the range within which the true population parameter is expected to fall.

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How does sample size affect the Margin of Error?

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As the sample size increases, the Margin of Error decreases, leading to more precise estimates of the population parameter.

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What happens to the Margin of Error if the standard deviation increases?

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If the standard deviation increases, the Margin of Error increases, indicating less precision in estimating the population parameter.

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What is a confidence interval?

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A confidence interval is a range of values, derived from a data set, that is likely to contain the value of an unknown population parameter.

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How do you calculate the Margin of Error?

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The Margin of Error can be calculated using the formula: MOE = z * (σ/√n), where z is the z-score corresponding to the desired confidence level, σ is the standard deviation, and n is the sample size.

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What does a 95% confidence interval mean?

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A 95% confidence interval means that if we were to take many samples and build a confidence interval from each sample, approximately 95% of those intervals would contain the true population parameter.

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If the sample mean is $5.50 and the MOE is $0.31, what is the confidence interval?

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The confidence interval is [$5.19, $5.81].

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What is the relationship between sample size and confidence level?

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Increasing the confidence level (e.g., from 95% to 99%) generally requires a larger sample size to maintain the same Margin of Error.

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What does it mean if the Margin of Error is large?

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A large Margin of Error indicates less confidence in the precision of the estimate, suggesting that the sample may not accurately reflect the population.

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What is the effect of increasing the confidence level on the Margin of Error?

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Increasing the confidence level results in a larger Margin of Error, as a wider range is needed to ensure that the true population parameter is captured.