Confidence Interval for the Mean (large sample)

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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 true population parameter (e.g., mean) with a specified level of confidence.

Tags

CCSS.HSS.IC.B.4

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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 mean.

Tags

CCSS.HSS.IC.B.4

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How do you calculate the confidence interval for the mean with a large sample?

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The confidence interval for the mean is calculated using the formula: CI = x̄ ± Z * (σ/√n), where x̄ is the sample mean, Z is the Z-value corresponding to the desired confidence level, σ is the standard deviation, and n is the sample size.

Tags

CCSS.HSS.IC.B.4

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What is the Z-value for a 99% confidence level?

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The Z-value for a 99% confidence level is approximately 2.576.

Tags

CCSS.HSS.ID.A.4

Front

What is the Z-value for a 95% confidence level?

Back

The Z-value for a 95% confidence level is approximately 1.96.

Tags

CCSS.HSS.ID.A.4

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What is the standard deviation?

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Standard deviation is a measure of the amount of variation or dispersion in a set of values.

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What is the relationship between sample size and confidence interval width?

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As the sample size increases, the width of the confidence interval decreases, leading to a more precise estimate of the population parameter.

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What happens to the confidence interval if the confidence level is increased?

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If the confidence level is increased, the width of the confidence interval also increases, resulting in a less precise estimate.

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What is the maximum error of estimate (margin of error)?

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The maximum error of estimate, or margin of error, is the maximum amount by which the sample estimate may differ from the true population parameter.

Tags

CCSS.HSS.IC.B.4

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How do you find the margin of error for a confidence interval?

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The margin of error is calculated as: ME = Z * (σ/√n), where Z is the Z-value for the desired confidence level, σ is the standard deviation, and n is the sample size.

Tags

CCSS.HSS.IC.B.4