What is a confidence interval and why is it important?

What is a confidence interval and why is it important?

A confidence interval is a range of values used to estimate the true value of a population parameter. It's important because it gives us an idea of how uncertain we are about our estimate.

How do you calculate a confidence interval?

To calculate a confidence interval, you typically use the formula: CI = ar{x} ± Z * (σ/√n), where ar{x} is the sample mean, Z is the Z-score, σ is the standard deviation, and n is the sample size.

What does the Z-score represent in this context?

The Z-score represents the number of standard deviations a data point is from the mean. It helps determine the width of the confidence interval based on the desired confidence level.

Can you give me an example of a confidence interval?

Sure! If you have a sample mean of 50, a standard deviation of 10, and a sample size of 100, a 95% confidence interval would be approximately 48 to 52.