Confidence Intervals Flashcard

Front

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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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* or t*) * (σ/√n), where x̄ is the sample mean, z* or t* is the critical value, σ is the standard deviation, and n is the sample size.

Front

What does the term 'degrees of freedom' refer to in statistics?

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Degrees of freedom refer to the number of independent values or quantities which can be assigned to a statistical distribution. For a sample, it is typically calculated as n - 1, where n is the sample size.

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What happens to the width of a confidence interval when the confidence level increases?

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When the confidence level increases, the confidence interval becomes wider. This is because a higher confidence level requires a larger margin of error to ensure that the true population parameter is captured.

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What is the critical value for a 90% confidence level with a sample size of 15?

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The critical value (t) for a 90% confidence level with a sample size of 15 is approximately 1.761.

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What is the standard deviation and why is it important in statistics?

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Standard deviation is a measure of the amount of variation or dispersion in a set of values. It is important because it provides insight into the reliability and variability of the data.

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How does sample size affect the 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 formula for calculating the margin of error in a confidence interval?

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The margin of error (ME) is calculated as ME = z* (σ/√n) for large samples or ME = t* (s/√n) for small samples, where z* or t* is the critical value, σ is the population standard deviation, s is the sample standard deviation, and n is the sample size.

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What does a 98% confidence interval indicate?

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A 98% confidence interval indicates that if we were to take many samples and build a confidence interval from each sample, approximately 98% of those intervals would contain the true population mean.

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What is the relationship between confidence level and sample size?

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Higher confidence levels require larger sample sizes to maintain the same margin of error, as larger samples provide more information about the population.