Confidence Interval Practice

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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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What does a larger confidence interval indicate?

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A larger confidence interval indicates a higher level of uncertainty about the estimate, but it also means a higher confidence level in capturing the true population parameter.

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What is the critical value in a confidence interval?

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The critical value is a factor used to compute the margin of error in a confidence interval. It corresponds to the desired confidence level and is derived from the standard normal distribution.

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How do you calculate the standard error?

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Standard error (SE) is calculated as the sample standard deviation (s) divided by the square root of the sample size (n): SE = s / √n.

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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, often the sample mean.

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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 parameter.

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If a confidence interval is (114.56, 125.54), what can we infer about the population mean?

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We can infer that the true population mean is likely to fall within the range of 114.56 to 125.54, and it is unlikely to be greater than 130.

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

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The formula for a confidence interval for the mean is: CI = sample mean ± (critical value * standard error).

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What is the relationship between sample size and confidence interval width?

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As the sample size increases, the width of the confidence interval decreases, leading to a more precise estimate of the population parameter.

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What does it mean if a confidence interval does not include zero?

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If a confidence interval does not include zero, it suggests that there is a statistically significant difference or effect present.