A statistical tool determines a range within which a population parameter, such as a mean, is likely to fall, given a sample from that population. This range is calculated using a specific formula that incorporates the sample’s standard deviation, its size, and a critical value from the t-distribution. For instance, analyzing test scores from a small group of students might yield a range suggesting the likely average score for the entire class.
Utilizing this approach is beneficial when the population standard deviation is unknown and the sample size is small, typically less than 30. It allows researchers to make inferences about a population with limited data, providing a degree of certainty in their estimates. Historically, this method became essential as statistical analysis expanded to fields where large-scale data collection was impractical or impossible.
