Confidence Interval (Practice)

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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 true value of an unknown population parameter, with a specified level of confidence.

Tags

CCSS.HSS.IC.B.4

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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 * (σ/√n)), where x̄ is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Tags

CCSS.HSS.IC.B.4

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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.

Tags

CCSS.HSS.IC.B.4

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What is the effect of increasing the sample size on the confidence interval?

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Increasing the sample size generally results in a narrower confidence interval, as it reduces the standard error of the mean.

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What is the effect of decreasing the confidence level on the confidence interval?

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Decreasing the confidence level results in a narrower confidence interval, as it reduces the z-score used in the calculation.

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What is the formula for the standard error of the mean?

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The standard error of the mean (SEM) is calculated as SEM = σ/√n, where σ is the population standard deviation and n is the sample size.

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What is the z-score for a 90% confidence level?

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The z-score for a 90% confidence level is approximately 1.645.

Tags

CCSS.HSS.ID.A.4

Front

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

Back

The z-score for a 95% confidence level is approximately 1.96.

Tags

CCSS.HSS.ID.A.4

Front

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

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The z-score for a 99% confidence level is approximately 2.576.

Tags

CCSS.HSS.ID.A.4

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Given a sample mean of 105.2 and a standard deviation of 10, calculate the 90% confidence interval for n=75.

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The 90% confidence interval is (103, 107).

Tags

CCSS.HSS.IC.B.4