Which statistical test is used to compare the means of two distributions when the population standard deviation is known?

The z-test is used to compare the means of two distributions when the population standard deviation is known. This test is applicable in scenarios where the sample size is large (typically n > 30), allowing the sample mean to be normally distributed according to the Central Limit Theorem.

The key aspect that distinguishes the z-test from other tests, such as the t-test, is the assumption of knowing the population standard deviation. When this information is available, the z-test provides a rigorous method to assess whether there are significant differences between the means of two groups. It utilizes the standard normal distribution to calculate the z-statistic, which then helps in determining the p-value for hypothesis testing.

In contrast, the t-test would be used when the population standard deviation is unknown, making it less suitable for this specific context. The F-test is primarily used to compare variances between two or more groups, while the Chi-squared test assesses categorical data, making them inappropriate choices in the context of comparing means.