Estimating a Mean

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What is the definition of 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 expressed with a certain level of confidence, such as 95% or 99%.

Front

What is the formula for calculating the standard error of the mean (SEM)?

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What does the term 'Large Counts condition' refer to in statistics?

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The Large Counts condition states that for a sample proportion to be approximately normally distributed, both np-hat and n(1-p-hat) must be greater than or equal to 10.

Front

How do you construct a confidence interval for a population mean when the population standard deviation is known?

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Front

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.

Front

What is the purpose of using a confidence interval in statistics?

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The purpose of using a confidence interval is to estimate the range within which a population parameter (like the mean) is likely to fall, providing a measure of uncertainty around the estimate.

Front

How do you interpret a 90% confidence interval?

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

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

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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.

Front

What is the formula for a confidence interval when the population standard deviation is unknown?

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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, depending on the context of the study.