Confidence Intervals

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What is a confidence interval?

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A confidence interval is a range of values, derived from sample statistics, 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 indicate?

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A 90% confidence interval indicates 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 does increasing the confidence level affect the width of the confidence interval?

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Increasing the confidence level results in a wider confidence interval because a higher level of confidence requires a larger margin of error to ensure that the true parameter is captured.

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What is the relationship between confidence level and margin of error?

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As the confidence level increases, the margin of error also increases, leading to a wider confidence interval.

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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 (E) can be calculated using the formula: E = z * (σ/√n), where z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Front

What is the z-score for a 95% confidence level?

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Front

What is the z-score for a 99% confidence level?

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Front

If the confidence interval is (120, 160), what is the mean?

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The mean is calculated as the average of the two endpoints: Mean = (120 + 160) / 2 = 140.

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How do you interpret a confidence interval of (120, 160)?

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A confidence interval of (120, 160) suggests that we are confident that the true population parameter lies between 120 and 160.

Front

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

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If the sample size increases, the confidence interval becomes narrower, assuming the confidence level remains the same, because the standard error decreases.