Flashcard-Understanding Margin of Error and 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 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.

Tags

CCSS.HSS.IC.B.4

Front

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.

Tags

CCSS.HSS.IC.B.4

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

Tags

CCSS.HSS.IC.B.4

Front

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.

Front

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.

Tags

CCSS.HSS.IC.B.4

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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.

Tags

CCSS.HSS.IC.B.4

Front

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%.

Tags

CCSS.HSS.IC.B.4

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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.

Tags

CCSS.HSS.IC.B.4

Front

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.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

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.

Tags

CCSS.HSS.IC.B.4