What is the primary function of a t-test?

The primary function of a t-test is to compare two means or a sample mean to a population mean, making it a widely used statistical method when determining if there is a significant difference between groups. The t-test evaluates whether the means of two datasets are statistically different from each other, indicating that the populations from which the samples are drawn may not be the same.

In practice, when you conduct a t-test, you typically have one of two scenarios: comparing the means of two independent groups (like testing the effectiveness of a new drug on one group versus a control group) or comparing the mean of a single sample against a known population mean. The test produces a t-value, which reflects the size of the difference relative to the variation observed in the sample data, allowing for meaningful interpretation of the results in the context of hypothesis testing.

Other choices do not capture the primary purpose of a t-test. While assessing variability within a single sample may pertain to statistical analysis, it is not the aim of a t-test. Analyzing the correlation between multiple variables refers to correlation analysis rather than mean comparison, and measuring the impact of randomization is associated with experimental design rather than the specific function of a t-test. Therefore, the t-test serves as a