Confidence Intervals Review

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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 a 90% confidence interval mean?

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A 90% confidence interval means that if we were to take many samples and build a confidence interval from each sample, approximately 90% of those intervals would contain the true population parameter.

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How do you calculate a confidence interval for a population mean?

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To calculate a confidence interval for a population mean, use the formula: CI = x̄ ± (z * (σ/√n)), where x̄ is the sample mean, 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 is the role of sample size in confidence intervals?

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

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What is the effect of increasing the confidence level on the confidence interval?

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Increasing the confidence level results in a wider confidence interval, as it requires a larger range to ensure that the true parameter is captured.

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What is the margin of error in a confidence interval?

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The margin of error is the amount added and subtracted from the sample statistic to create the confidence interval. It reflects the uncertainty associated with the sample estimate.

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What is the difference between a sample mean and a population mean?

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The sample mean is the average of a subset of data, while the population mean is the average of all possible data points in the entire population.

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What does it mean if a confidence interval does not include a certain value?

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If a confidence interval does not include a certain value, it suggests that there is not enough evidence to support that the population parameter is equal to that value.

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How do you interpret a confidence interval?

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To interpret a confidence interval, you can say, 'We are C% confident that the interval from ___ to ___ captures the true [parameter in context].' This means that the interval is likely to contain the true value.

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What is the standard deviation's role in calculating confidence intervals?

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The standard deviation measures the amount of variation or dispersion in a set of values. It is used in the calculation of the confidence interval to account for variability in the data.