Flashcard-Understanding Margin of Error and Confidence Intervals

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 is the sample mean related to a confidence interval?

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The sample mean is the midpoint of the confidence interval. It is calculated as the average of the lower and upper bounds of the interval.

Front

What is the formula for calculating the margin of error in a confidence interval?

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The margin of error is calculated as half the width of the confidence interval. It can be expressed as: Margin of Error = (Upper Limit - Lower Limit) / 2.

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If a confidence interval is (40, 60), what is the sample mean?

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The sample mean is 50, which is the midpoint of the interval.

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If a confidence interval is (40, 60), what is the margin of error?

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The margin of error is 10, calculated as (60 - 40) / 2.

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What does a wider confidence interval indicate about the margin of error?

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A wider confidence interval indicates a larger margin of error, suggesting greater uncertainty about the population parameter.

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What is the significance of the confidence level in a confidence interval?

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The confidence level represents the probability that the confidence interval contains the true population parameter. Common levels are 90%, 95%, and 99%.

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How does sample size affect the margin of error?

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As the sample size increases, the margin of error decreases, leading to a more precise confidence interval.

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What is the relationship between confidence intervals and hypothesis testing?

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Confidence intervals can be used in hypothesis testing to determine if a null hypothesis can be rejected based on whether the hypothesized value falls within the interval.

Front

If a confidence interval is (150, 210), what is the margin of error?

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The margin of error is 30, calculated as (210 - 150) / 2.