Confidence Intervals Flashcard

Front

What is a confidence interval?

Back

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 used to estimate the uncertainty around a sample statistic.

Front

What does a 95% confidence interval mean?

Back

A 95% confidence interval means that if we were to take 100 different samples and compute a confidence interval for each sample, approximately 95 of the 100 confidence intervals will contain the true population mean.

Front

How do you interpret a confidence interval?

Back

A confidence interval is interpreted as the range within which we expect the true population parameter to lie, with a certain level of confidence (e.g., 90%, 95%, 99%).

Front

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

Back

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

Front

What is the z-value for a 90% confidence interval?

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The z-value for a 90% confidence interval is approximately 1.645.

Front

What is the z-value for a 95% confidence interval?

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The z-value for a 95% confidence interval is approximately 1.96.

Front

What is the z-value for a 98% confidence interval?

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The z-value for a 98% confidence interval is approximately 2.33.

Front

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

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The standard error of the mean (SEM) is the standard deviation of the sampling distribution of the sample mean, calculated as SEM = σ/√n.

Front

How does sample size affect the 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 relationship between confidence level and interval width?

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As the confidence level increases (e.g., from 90% to 95%), the width of the confidence interval also increases, reflecting greater uncertainty.