AP Statistics: Confidence Intervals

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What is a confidence interval?

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A range of values used to estimate a population parameter, constructed from sample data.

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What are the conditions for constructing a confidence interval for one sample proportion?

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1. Random sample. 2. Large enough sample size (np ≥ 10 and n(1-p) ≥ 10). 3. Population is at least 10 times the sample size.

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What are the conditions for constructing a confidence interval for two sample proportions?

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1. Independent random samples. 2. Large enough sample sizes for both groups (n1p1, n1(1-p1), n2p2, n2(1-p2) all ≥ 10). 3. Populations are at least 10 times the sample sizes.

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What are the conditions for constructing a confidence interval for one sample mean?

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1. Random sample. 2. Normal distribution of the population or large sample size (n ≥ 30). 3. Population is at least 10 times the sample size.

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What are the conditions for constructing a confidence interval for two sample means?

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1. Independent random samples. 2. Normal distribution of both populations or large sample sizes (n1, n2 ≥ 30). 3. Populations are at least 10 times the sample sizes.

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What is a sentence frame for interpreting a confidence interval for a proportion?

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"We are [confidence level]% confident that the true proportion of [context] is between [lower bound] and [upper bound]."

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What is a sentence frame for interpreting a confidence interval for a mean?

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"We are [confidence level]% confident that the true mean of [context] is between [lower bound] and [upper bound]."

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What factors affect the width of a confidence interval?

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The width of a confidence interval is affected by the sample size, the variability in the data, and the confidence level. Larger sample sizes and lower variability result in narrower intervals, while higher confidence levels result in wider intervals.

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What is the confidence interval formula for 1 sample proportions?

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What is the formula for a 2 sample difference in proportions confidence interval?

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