Confidence Intervals
Definition
Confidence intervals are ranges of values calculated from sample data that are likely to contain an unknown population parameter with a certain level of confidence.
Analogy
Imagine you have a bag of marbles, but you don't know how many there are. You take multiple samples and calculate confidence intervals to estimate how many marbles are in the bag. The wider your interval, the less confident you can be about your estimate.
Related terms
Margin of Error: The margin of error is half the width of a confidence interval and represents how much we expect our estimate to vary from sample to sample.
Level of Confidence: The level of confidence determines how sure we want to be that our confidence interval contains the true parameter value. Common levels include 90%, 95%, and 99%.
Sample Size: Increasing sample size generally leads to narrower confidence intervals because more data reduces uncertainty.
"Confidence Intervals" appears in:
Study guides (3)
Additional resources (2)
Practice Questions (5)
- What does the Central Limit Theorem state in the context of constructing confidence intervals?
- Which of the following statements about confidence intervals is true?
- When comparing confidence intervals for the difference of two means, what tends to happen to the width of the interval as the sample sizes increase?
- In repeated random sampling with the same sample size, what percentage of confidence intervals will capture the population proportion?
- What is a good template to use for interpreting confidence intervals?
Resources
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.