Confidence Intervals for Means: The Basics

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What are confidence intervals?

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Confidence intervals are a range of values, derived from sample statistics, that are likely to contain the value of an unknown population parameter. They provide an estimate of uncertainty around a sample statistic.

Tags

CCSS.HSS.IC.B.4

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What is a critical z-value?

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A critical z-value is a point on the standard normal distribution that corresponds to a specified level of confidence. It is used to determine the margin of error in confidence intervals.

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CCSS.HSS.ID.A.4

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What are the critical z-values for a 99% confidence interval?

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CCSS.HSS.ID.A.4

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What are the critical z-values for a 95% confidence interval?

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CCSS.HSS.ID.A.4

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What are the critical z-values for an 80% confidence interval?

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Tags

CCSS.HSS.ID.A.4

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What does a 90% confidence interval mean?

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A 90% confidence interval means that we are 90% confident that the population mean lies within the interval boundaries.

Tags

CCSS.HSS.IC.B.4

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

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Tags

CCSS.HSS.IC.B.4

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What is the difference between z-distribution and t-distribution?

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The z-distribution is used when the population variance is known or the sample size is large (n > 30), while the t-distribution is used when the population variance is unknown and the sample size is small (n ≤ 30).

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What are the critical t-values for a 98% confidence interval with a sample size of 4?

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How does sample size affect 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.