6.1-6.3 Practice - Confidence Intervals for Proportions

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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. It is expressed with a confidence level, such as 90% or 95%.

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What is the formula for calculating a confidence interval for a proportion?

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The formula is: Confidence Interval = point estimate ± margin of error, where margin of error = critical value × standard error.

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What does the term 'point estimate' refer to in statistics?

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A point estimate is a single value estimate of a population parameter, such as the sample proportion.

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What is the margin of error in the context of confidence intervals?

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The margin of error is the range of values above and below the point estimate that reflects the uncertainty of the estimate.

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How do you find the critical value for a given confidence level?

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The critical value can be found using a Z-table or t-table, depending on the sample size and whether the population standard deviation is known.

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What is the standard error of a proportion?

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The standard error of a proportion is calculated as: SE = sqrt[(p(1-p)/n)], where p is the sample proportion and n is the sample size.

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What is the significance of a 90% confidence level?

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A 90% confidence level means that if we were to take 100 different samples and compute a confidence interval for each sample, approximately 90 of the intervals would contain the true population proportion.

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How do you interpret a confidence interval?

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A confidence interval provides a range of plausible values for the population parameter. For example, if the 90% confidence interval for a proportion is (0.621, 0.780), we are 90% confident that the true proportion lies within this range.

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What is the difference between a one-sample and a two-sample confidence interval?

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A one-sample confidence interval estimates a single population parameter, while a two-sample confidence interval compares the parameters of two different populations.

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What is the purpose of using a higher confidence level?

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Using a higher confidence level increases the range of the confidence interval, providing more certainty that the interval contains the true parameter, but it also makes the interval wider.