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.

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What does a 99% confidence interval indicate?

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A 99% confidence interval indicates that if we were to take many samples and build a confidence interval from each sample, approximately 99% of those intervals would contain the true population parameter.

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What is the critical value for a 99% confidence interval?

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The critical value for a 99% confidence interval is approximately 2.575.

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How does the width of a 99% confidence interval compare to a 90% confidence interval?

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A 99% confidence interval is wider than a 90% confidence interval because it requires a higher level of certainty, which increases the range of values.

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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 of error that is allowed in the estimate of the population parameter, often denoted by the symbol 'E'.

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What is the formula for calculating the Margin of Error?

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The Margin of Error (E) can be calculated using the formula: E = critical value * standard error.

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What does p-hat represent in statistics?

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p-hat (√) is the symbol used to represent the sample proportion, which is the number of successes divided by the total number of trials.

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How do you calculate p-hat from a sample?

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p-hat is calculated by dividing the number of successes in the sample by the total number of observations in the sample.

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What is the confidence interval statement for an interval of (0.75, 0.87) at a 95% confidence level?

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With 95% confidence, the true proportion of the population is between 75% and 87%.

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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 chosen.