Final answer:
The most appropriate test for Lea's study on height differences between right-handed and left-handed students is a two-sample t-test. The alternative hypothesis depends on her presumption about the direction of the difference, hence option C is apt if she assumes right-handed students are taller.
Step-by-step explanation:
Lea is interested in testing the difference in average height between right-handed and left-handed students at her school. Because she is comparing two independent groups (right-handed and left-handed students) rather than a paired or matched sample, a two-sample t-test is the most appropriate. The null hypothesis (H0) would state that there is no difference in the average heights, which can be represented as H0: μright-handed = μleft-handed. The alternative hypothesis (Ha) should reflect the claim Lea wants to test. If she does not have a direction in mind, she would use Ha: μright-handed ≠ μleft-handed for a two-tailed test. Suppose Lea believes that right-handed students are taller on average; her Ha would be Ha: μright-handed > μleft-handed, indicating a right-tailed test. If she believes left-handed students are taller, it would be Ha: μright-handed < μleft-handed, a left-tailed test. This information suggests that option C, 'Two-sample t-test with Ha: μright-handed > μleft-handed' is appropriate if Lea suspects that right-handed students are taller.