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

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Multiple Choice

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

Explanation:
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.

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