Confidence Intervals using a T-Distribution

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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 true value of an unknown population parameter, with a specified level of confidence.

Tags

CCSS.HSS.IC.B.4

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What does a 90% confidence level mean?

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A 90% confidence level means that if we were to take 100 different samples and compute a confidence interval for each sample, approximately 90 of the intervals would contain the true population mean.

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CCSS.HSS.IC.B.4

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How is a confidence interval constructed using a t-distribution?

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A confidence interval using a t-distribution is constructed by taking the sample mean, adding and subtracting the product of the t-score (from the t-distribution table) and the standard error of the mean.

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CCSS.HSS.IC.B.4

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

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The standard error of the mean (SEM) is calculated as SEM = s / √n, where s is the sample 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 is the average of a subset of data, while the population mean is the average of all possible data points in the entire population.

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CCSS.6.SP.A.3

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What does it mean to be '95% confident' in a confidence interval?

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Being '95% confident' means that there is a 95% probability that the confidence interval calculated from the sample data contains the true population mean.

Tags

CCSS.HSS.IC.B.4

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What is the t-distribution and when is it used?

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The t-distribution is a type of probability distribution that is used when estimating population parameters when the sample size is small (typically n < 30) and/or the population standard deviation is unknown.

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How do you interpret a confidence interval?

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A confidence interval is interpreted as the range within which we expect the true population parameter to lie, based on the sample data and the specified confidence level.

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CCSS.7.SP.C.5

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What is the significance of the sample size in constructing a confidence interval?

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A larger sample size generally results in a narrower confidence interval, indicating more precision in estimating the population parameter.

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What is the role of the critical value in confidence intervals?

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The critical value is a factor used to compute the margin of error in a confidence interval, determined by the desired confidence level and the sample size.

Tags

CCSS.HSS.IC.B.4