Final answer:
The null hypothesis in a two-sample t-test states that two population means are equal (H0: μ1 = μ2), while the alternative hypothesis suggests they are different (Ha: μ1 ≠ μ2). The direction of the test (right, left, or two-tailed) depends on the nature of the research question.
Step-by-step explanation:
Hypotheses in a Two-Sample t-Test:
In a two-sample t-test, the null hypothesis (H0) asserts that the means of two populations are equal. Symbolically, this is represented as H0: μ1 = μ2, where μ1 and μ2 are the population means. The alternative hypothesis (Ha) suggests that there is a difference between the population means, which can be represented as Ha: μ1 ≠ μ2. This test could be right-tailed, left-tailed, or two-tailed based on the direction of the hypothesis.
The null hypothesis is based on the premise that any observed difference in sample means is due to sampling variability and not due to a genuine difference in the population means. Conversely, the alternative hypothesis directly challenges this by positing that the observed differences are indicative of true differences in the population means.