Confidence Interval introduction

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 true population parameter (e.g., mean) with a specified level of confidence.

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What does a 95% Confidence Interval indicate?

Back

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 parameter.

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What is the formula for a Confidence Interval for a population mean?

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The formula is: Point Estimate ± Margin of Error.

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What is Margin of Error?

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Margin of Error is the range of values above and below the point estimate that reflects the uncertainty in the estimate.

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How do you calculate Margin of Error?

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Margin of Error = Critical Value × Standard Error.

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What is a Critical Value in the context of Confidence Intervals?

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A Critical Value is a factor used to compute the margin of error, which corresponds to the desired confidence level.

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What is Standard Error?

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Standard Error is the standard deviation of the sampling distribution of a statistic, commonly the mean.

Front

If a 95% Confidence Interval for a mean is (114.56, 125.54), can we conclude that the true mean is greater than 130?

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No, because 130 is outside the interval.

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Does the interval (3, 14) support the claim that the mean of a data set is 2.9?

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No, because 2.9 is outside the interval.

Front

What happens to the Confidence Interval as the confidence level increases?

Back

As the confidence level increases, the Confidence Interval becomes wider.