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 value of an unknown population parameter. It is used to estimate the uncertainty around a sample statistic.

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What is the point estimate in statistics?

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The point estimate is a single value estimate of a population parameter, such as the sample mean, which serves as the best guess of the true parameter.

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How do you calculate the margin of error for a confidence interval?

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Margin of error = Critical value * Standard error. The critical value corresponds to the desired confidence level, and the standard error is the standard deviation divided by the square root of the sample size.

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What does a 90% confidence interval mean?

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A 90% confidence interval means that if we were to take many samples and build a confidence interval from each sample, approximately 90% of those intervals would contain the true population mean.

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What is the standard error?

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The standard error is the standard deviation of the sampling distribution of a statistic, commonly the mean. It measures how much the sample mean is expected to vary from the true population mean.

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What is the critical value in the context of confidence intervals?

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The critical value is a factor used to compute the margin of error, based on the desired confidence level. It is derived from the standard normal distribution (Z-distribution) or t-distribution.

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How does sample size affect the margin of error?

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As the sample size increases, the margin of error decreases, leading to a more precise confidence interval. This is because larger samples provide more information about the population.

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What is the relationship between confidence level and margin of error?

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As the confidence level increases, the margin of error also increases. A higher confidence level means a wider interval to ensure the true parameter is captured.

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What is the formula for a confidence interval for the mean?

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Confidence interval = Sample mean ± Margin of error.

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What is the significance of a 99% confidence interval?

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A 99% confidence interval indicates that there is a 99% chance that the interval contains the true population parameter, providing a higher level of certainty than lower confidence levels.