AP Statistics Ch 19 Confidence Interval for Proportions MU

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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 do you calculate a confidence interval for a proportion?

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To calculate a confidence interval for a proportion, use the formula: CI = p̂ ± Z * √(p̂(1-p̂)/n), where p̂ is the sample proportion, Z is the Z-score corresponding to the desired confidence level, and n is the sample size.

Front

What does the Z-score represent in a confidence interval?

Back

The Z-score represents the number of standard deviations a data point is from the mean. In the context of confidence intervals, it corresponds to the desired confidence level (e.g., 1.96 for 95% confidence).

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What is the significance of sample size in confidence intervals?

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Larger sample sizes generally lead to narrower confidence intervals, indicating more precise estimates of the population parameter.

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What is the formula for the sample proportion (p̂)?

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The sample proportion (p̂) is calculated as p̂ = x/n, where x is the number of successes (e.g., left-handed individuals) and n is the total sample size.

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

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Increasing the confidence level results in a wider confidence interval, as it requires a larger margin of error to ensure that the interval captures the true population parameter.

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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 value falls within the interval. If it does, we fail to reject the null hypothesis.

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What is the margin of error in a confidence interval?

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The margin of error is the amount added and subtracted from the sample proportion to create the confidence interval. It reflects the uncertainty in the estimate.

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How does randomness affect the variability of a confidence interval?

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Increasing randomness in sampling can help reduce variability in the confidence interval, leading to more reliable estimates.

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What is the purpose of using a confidence interval?

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The purpose of using a confidence interval is to provide a range of plausible values for a population parameter, allowing for uncertainty in the estimate.