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. A larger sample provides more accurate estimates of 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 sample statistics, that is likely to contain the value of an unknown population parameter.

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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 100 different samples and compute a confidence interval for each sample, approximately 95 of the intervals would contain the true population mean.

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What is the formula for calculating the Margin of Error?

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The Margin of Error (MOE) 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 population standard deviation, and n is the sample size.

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What happens to the MOE if the standard deviation increases?

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If the standard deviation increases, the Margin of Error (MOE) will also increase, indicating a wider range of uncertainty in the estimate.

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What is the relationship between confidence level and Margin of Error?

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As the confidence level increases, the Margin of Error also increases. A higher confidence level means a wider interval to ensure the true parameter is captured.

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How do you interpret a confidence interval of [15.54, 16.86]?

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This confidence interval suggests that we are 95% confident that the true mean assembly time for all workers lies between 15.54 and 16.86 minutes.

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What is the significance of the sample mean in constructing a confidence interval?

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The sample mean is the central point around which the confidence interval is constructed. It serves as the best estimate of the population mean.

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What is the effect of a smaller sample size on the MOE?

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A smaller sample size results in a larger Margin of Error (MOE), indicating less precision in estimating the population parameter.