Confidence interval

Definition

A confidence interval is a range of values, derived from sample data, that is likely to contain the population mean. It provides an estimate of the uncertainty surrounding that mean.

5 Must Know Facts For Your Next Test

1. A confidence interval for a single population mean using the Student t distribution accounts for small sample sizes.
2. The width of the confidence interval depends on the standard deviation, sample size, and confidence level.
3. As the sample size increases, the t-distribution approaches a normal distribution.
4. The critical value from the t-distribution varies based on degrees of freedom and desired confidence level.
5. Commonly used confidence levels are 90%, 95%, and 99%.

Review Questions

• What factors affect the width of a confidence interval?
• Why would you use a Student t distribution instead of a normal distribution when creating a confidence interval?
• How does increasing the sample size impact the confidence interval?

Related terms

Student t Distribution: A probability distribution used in statistical inference for estimating population parameters when the sample size is small.

Degrees of Freedom: The number of independent values or quantities which can be assigned to a statistical distribution.

Standard Error: An estimate of the standard deviation of the sampling distribution of a statistic.