State the null and alternative hypotheses for a two-sample t-test.

State the null and alternative hypotheses for a two-sample t-test.

• A. H0: μ1 = μ2; H1: μ1 ≠ μ2 (two-sided) or μ1 > μ2 / μ1 < μ2 (one-sided).
• B. H0: μ1 ≠ μ2; H1: μ1 = μ2.
• C. H0: μ1 > μ2; H1: μ1 ≤ μ2.
• D. H0: All groups have equal variances; H1: Not all variances are equal.

Answer: (A)

Two-sample t-tests are used to compare the population means of two independent groups. The null hypothesis asserts that the two population means are equal, μ1 = μ2. The alternative hypothesis states that there is a difference in the means: μ1 ≠ μ2 for a two-sided test, or μ1 > μ2 or μ1 < μ2 for a one-sided test. This framing directly targets whether the two groups come from populations with the same mean or different means. The other options miss the standard setup: they either flip which statement is null versus alternative, or they compare variances instead of means, which isn’t what a two-sample t-test assesses.

Two-sample t-tests are used to compare the population means of two independent groups. The null hypothesis asserts that the two population means are equal, μ1 = μ2. The alternative hypothesis states that there is a difference in the means: μ1 ≠ μ2 for a two-sided test, or μ1 > μ2 or μ1 < μ2 for a one-sided test. This framing directly targets whether the two groups come from populations with the same mean or different means.

The other options miss the standard setup: they either flip which statement is null versus alternative, or they compare variances instead of means, which isn’t what a two-sample t-test assesses.