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 associated with a confidence level that quantifies the level of confidence that the parameter lies within the interval.

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What does Standard Error (SE) represent?

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Standard Error (SE) measures the accuracy with which a sample represents a population. It is the standard deviation of the sampling distribution of a statistic, commonly the mean.

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How do you calculate Standard Error for a sample mean?

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Standard Error (SE) is calculated using the formula: SE = σ / √n, where σ is the population standard deviation and n is the sample size.

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What is the formula for Margin of Error (ME) in a confidence interval?

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Margin of Error (ME) is calculated using the formula: ME = z * SE, where z is the z-score corresponding to the desired confidence level and SE is the standard error.

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What is the z-score for a 90% confidence level?

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The z-score for a 90% confidence level is approximately 1.645.

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What is the z-score for a 99% confidence level?

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The z-score for a 99% confidence level is approximately 2.576.

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True or False: Increasing the confidence level will result in a wider confidence interval.

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True. A higher confidence level means a wider interval to ensure the population parameter is captured.

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How do you construct a Confidence Interval for the population mean?

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To construct a Confidence Interval for the population mean, use the formula: CI = (sample mean - ME, sample mean + ME), where ME is the margin of error.

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What is the relationship between sample size and Standard Error?

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As the sample size increases, the Standard Error decreases, leading to a more precise estimate of the population parameter.

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What is the effect of sample standard deviation on the Confidence Interval?

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A larger sample standard deviation results in a wider confidence interval, indicating more variability in the data.