TC Flashcard on Confidence Interval

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What is a confidence interval?

Back

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 used to estimate the uncertainty around a sample statistic.

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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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How do you calculate the sample mean?

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The sample mean is calculated by adding all the sample values together and dividing by the number of samples.

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

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The formula for a confidence interval for the mean is: CI = sample mean ± (critical value) * (standard deviation / √n), where n is the sample size.

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What is the critical value in a confidence interval?

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The critical value is a factor used to compute the margin of error in a confidence interval. It is determined by the desired confidence level and the distribution of the data.

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What happens to the confidence interval when the sample size increases?

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As the sample size increases, the confidence interval becomes narrower, indicating a more precise estimate of the population parameter.

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What is the relationship between confidence level and confidence interval width?

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Higher confidence levels result in wider confidence intervals, while lower confidence levels result in narrower intervals.

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What does it mean if a confidence interval does not contain the population mean?

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If a confidence interval does not contain the population mean, it suggests that the sample may not be representative of the population, or that the sample size is too small.

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What is a point estimate?

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A point estimate is a single value estimate of a population parameter, such as the sample mean.

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What is the margin of error in a confidence interval?

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The margin of error is the range of values above and below the sample statistic in a confidence interval, indicating the uncertainty of the estimate.