P&S: Confidence Intervals (Large Samples)

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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. It is associated with a confidence level that quantifies the level of confidence that the parameter lies within the interval.

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What does the margin of error represent in a confidence interval?

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The margin of error is the amount of error that is allowed in the estimation of a population parameter. It indicates the range within which the true population parameter is expected to lie, given a certain level of confidence.

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

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Margin of Error = Critical Value (Zc) * Standard Error (SE). The critical value corresponds to the desired confidence level, and the standard error is calculated as the population standard deviation divided by the square root of the sample size.

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What is the formula for the standard error of the mean (SEM)?

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Standard Error (SE) = σ / √n, where σ is the population standard deviation and n is the sample size.

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What is the critical value Zc for a 99% confidence level?

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The critical value Zc for a 99% confidence level is approximately 2.576.

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What is the critical value Zc for a 90% confidence level?

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The critical value Zc for a 90% confidence level is approximately 1.645.

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What is the point estimate in a confidence interval?

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The point estimate is the single best estimate of the population parameter, typically represented by the sample mean.

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How does sample size affect the width of a confidence interval?

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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 is the relationship between confidence level and the width of a confidence interval?

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Higher confidence levels result in wider confidence intervals, as they require a larger margin of error to ensure that the true parameter is captured within the interval.

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What is the formula for constructing a confidence interval for the population mean?

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Confidence Interval = Sample Mean ± Margin of Error.