Flashcard--Confidence Interval and Margin of Error

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 the margin of error represent in a confidence interval?

Back

The margin of error represents the maximum expected difference between the true population parameter and a sample estimate. It quantifies the uncertainty in the estimate.

Front

How is the margin of error calculated?

Back

The margin of error is calculated as the critical value (z* or t*) multiplied by the standard error of the sample mean.

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 estimate of the population parameter.

Front

What effect does increasing the confidence level have on the width of a confidence interval?

Back

Increasing the confidence level results in a wider confidence interval, as it requires a larger margin of error to ensure that the true parameter is captured.

Front

If a confidence interval is (75, 85), what is the sample mean?

Back

The sample mean is the midpoint of the confidence interval, which is (75 + 85) / 2 = 80.

Front

What happens to the width of a confidence interval if the population standard deviation increases?

Back

If the population standard deviation increases, the width of the confidence interval also increases, assuming the sample size and confidence level remain constant.

Front

How do you interpret a 95% confidence interval?

Back

A 95% confidence interval means 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.

Front

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

Back

The formula is: Confidence Interval = Sample Mean ± (Critical Value * Standard Error).

Front

What does a margin of error of 4 around a sample mean of 50 indicate?

Back

It indicates that the true population mean is likely to fall between 46 and 54.