What is the null hypothesis for a t-test comparing two means?

• A. The means are equal (no difference) between the two groups
• B. The means are different between the groups
• C. The variances are equal
• D. The samples come from the same population

Answer: (A)

In a t-test that compares two means, the null hypothesis is that there is no difference between the population means. In symbols, it states μ1 = μ2, meaning any observed difference in sample means is due to random sampling variability rather than a real difference in the populations. The test assesses whether the observed gap is larger than would be expected by chance. If the data show a statistically significant difference, you’d reject the null in favor of an alternative that the means differ (two-sided: μ1 ≠ μ2; one-sided: μ1 > μ2 or μ1 < μ2). The other statements aren’t the null itself: equality of variances is an assumption for a version of the test, not the null; and “samples from the same population” is a broader idea, while the precise null focuses specifically on equality of the population means.