What statistical test is used to compare a sample's proportion to a historic proportion?

The one-proportion test is specifically designed to compare the proportion of a sample to a known or historic proportion. This statistical test evaluates whether the observed proportion in a sample significantly differs from a specified historic proportion. For instance, if a company wants to know if the proportion of defects in a new batch of products is different from the historical defect rate, the one-proportion test would be the appropriate choice.

This test involves formulating a null hypothesis that states the sample proportion is equal to the historic proportion, and then using sample data to calculate a test statistic that will tell us if we have enough evidence to reject that null hypothesis at a given significance level. It focuses on a single sample rather than comparing two different groups, which makes it the right choice for scenarios that involve estimating how a single variable behaves against its known proportion.

While the two-proportion test compares proportions from two distinct samples, the chi-square test is often used to analyze categorical data and assess how observed counts differ from expected counts, not specifically for a single sample proportion against a historical figure. A variance test is unrelated to proportions, as it is concerned with the spread or variability of data within a sample or between groups, rather than proportions themselves.