If 20 students are divided into two groups of 10 to test the effect of red bull on running speed, what test is appropriate?

The appropriate test in this scenario is the unpaired t test. This statistical procedure is suitable when comparing the means of two independent groups. In this case, each group consists of 10 students who are exposed to different conditions—in this instance, testing the effect of Red Bull on running speed. Because the groups do not share any participants, the unpaired t test allows researchers to determine if there is a significant difference in running speeds between those who consumed Red Bull and those who did not.

Using the unpaired t test is essential for understanding whether the intervention (Red Bull consumption) had a significant effect on performance, based on the independent nature of the groups. Each student's performance is measured without being paired with any corresponding measurement from the other group, which is what makes the unpaired t test the correct choice for this scenario.

The other tests listed, such as the dependent (paired) t test, are not applicable here because they are meant for situations where the same subjects are measured under different conditions. ANOVA is used when comparing more than two groups, and correlation tests assess relationships between variables rather than mean differences. Thus, the unpaired t test aligns best with the study's design and objectives.