Creating 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, with a certain level of confidence (e.g., 95% or 99%).

Front

How do you calculate the mean of a sample?

Back

Front

What is the formula for a confidence interval for the mean when the population standard deviation is known?

Back

Front

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

Back

The z-score for a 95% confidence level is approximately 1.96.

Front

What is the z-score for a 99% confidence level?

Back

The z-score for a 99% confidence level is approximately 2.576.

Front

What does it mean if a confidence interval is (150, 350)?

Back

It means we are 95% confident that the true population mean lies between 150 and 350.

Front

How does sample size affect the width of a confidence interval?

Back

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 confidence interval width?

Back

As the confidence level increases, the width of the confidence interval also increases, providing a wider range to ensure the population parameter is captured.

Front

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

Back

Front

What is the interpretation of a 99% confidence interval?

Back

If we were to take many samples and construct a confidence interval from each sample, approximately 99% of those intervals would contain the true population mean.