Confidence interval

Definition

A confidence interval is a range of values, derived from sample data, that is likely to contain the value of an unknown population parameter. It provides an estimated range that is believed to contain the parameter with a certain level of confidence.

5 Must Know Facts For Your Next Test

1. A 95% confidence interval means there is a 95% chance that the interval contains the true population parameter.
2. The width of a confidence interval depends on the sample size and variability within the data; larger samples produce narrower intervals.
3. When the population standard deviation is unknown, the t-distribution is used instead of the normal distribution, especially for small samples.
4. The formula for a confidence interval when using the sample standard deviation includes $\bar{x} \pm t_{\alpha/2} \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $t_{\alpha/2}$ is the critical value from the t-distribution, s is the sample standard deviation, and n is the sample size.
5. In regression analysis, prediction intervals use similar principles but account for both model uncertainty and individual prediction error.

Review Questions

• What does a 95% confidence interval represent?
• How does increasing sample size affect a confidence interval?
• When should you use a t-distribution instead of a normal distribution for constructing a confidence interval?

Related terms

Population Parameter: A characteristic or measure of an entire population, as opposed to a statistic derived from a sample.

T-Distribution: A probability distribution used when estimating population parameters when the sample size is small and/or population variance is unknown.

Regression Analysis: A statistical technique for modeling and analyzing relationships between dependent and independent variables.