Confidence Intervals

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 expressed with a confidence level, such as 95%.

Front

What does a 95% confidence level indicate?

Back

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

Front

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

Back

Front

How do you calculate the margin of error for a confidence interval?

Back

Front

What is the z-score for a 95% confidence level?

Back

Front

If the sample mean is 142.5 and the margin of error is 5.2, what is the confidence interval?

Back

The confidence interval is (137.3, 147.7).

Front

What is the definition of margin of error?

Back

The margin of error is the amount added and subtracted from the sample statistic to create a confidence interval.

Front

How do you find the margin of error for a sample of 30 with a mean height of 62.3 in and a standard deviation of 1.5 in at 95% confidence?

Back

The margin of error is 0.56.

Front

What is the purpose of a confidence interval?

Back

The purpose of a confidence interval is to provide an estimated range of values which is likely to include an unknown population parameter, allowing for uncertainty in the estimate.

Front

What is the relationship between sample size and margin of error?

Back

As the sample size increases, the margin of error decreases, leading to a more precise confidence interval.