Confidence Interval with Means Review

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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 a 95% confidence interval indicate?

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A 95% confidence interval indicates that if we were to take many samples and build a confidence interval from each sample, approximately 95% of those intervals would contain the true population mean.

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What is the Central Limit Theorem?

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The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution, as long as the sample size is sufficiently large (usually n ≥ 30).

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What is the significance of sample size in confidence intervals?

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Larger sample sizes generally lead to narrower confidence intervals, providing a more precise estimate of the population parameter.

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How do you interpret a confidence interval of (1.80, 3.85) hours?

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This interval suggests that we are confident that the true mean time managers spend on paperwork lies between 1.80 and 3.85 hours.

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What does it mean if a value is not included in a confidence interval?

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If a value is not included in a confidence interval, it suggests that this value is not a plausible estimate of the population parameter based on the sample data.

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

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The formula is: CI = x̄ ± z*(σ/√n), where x̄ is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

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What is the difference between a sample mean and a population mean?

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The sample mean (x̄) is the average of a sample taken from a population, while the population mean (μ) is the average of all possible values in the entire population.

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What does it mean for a distribution to be skewed?

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A skewed distribution is one where the data points are not symmetrically distributed around the mean, leading to a longer tail on one side of the distribution.

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What is the role of the z-score in confidence intervals?

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The z-score represents the number of standard deviations a data point is from the mean and is used to determine the width of the confidence interval based on the desired confidence level.