What is the difference between confidence and prediction intervals?

What is the difference between confidence and prediction intervals?

Confidence intervals estimate the range in which a population parameter lies, while prediction intervals estimate the range for future observations.

Can you give me an example of each?

Sure! A confidence interval might say that we are 95% confident the true mean lies between 10 and 20. A prediction interval might say that we expect a future observation to fall between 5 and 25.

Why are prediction intervals wider than confidence intervals?

Prediction intervals are wider because they account for both the uncertainty in estimating the mean and the variability of individual observations.

How do I calculate these intervals?

To calculate a confidence interval, use the sample mean, standard error, and a critical value from the t-distribution. For prediction intervals, add the variability of individual data points to the confidence interval.