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.

Tags

CCSS.HSS.IC.B.4

Front

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.

Tags

CCSS.HSS.IC.B.4

Front

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

Back

The formula is: Point Estimate ± Margin of Error.

Tags

CCSS.HSS.IC.B.4

Front

What is Margin of Error?

Back

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

Tags

CCSS.HSS.IC.B.4

Front

How do you calculate Margin of Error?

Back

Margin of Error = Critical Value × Standard Error.

Tags

CCSS.HSS.IC.B.4

Front

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

Back

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

Tags

CCSS.HSS.IC.B.4

Front

What is Standard Error?

Back

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?

Back

No, because 130 is outside the interval.

Tags

CCSS.HSS.IC.B.4

Front

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

Back

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.