Final answer:
The dependent t-test is used to compare means of related samples, such as in pretest-posttest designs or when assessing the same subjects under two different conditions. It is appropriate for paired measurements on the same subjects, with null and alternative hypotheses stating no difference and a significant difference between the means, respectively.
Step-by-step explanation:
To choose the dependent t-test, consider a research scenario where you are interested in comparing the means of related samples. A common example is to test for significant difference in a pretest-posttest situation where the same subjects are tested before and after a treatment or intervention. Another scenario could be comparing the mean scores of two time periods or conditions for the same group of subjects. The dependent t-test is appropriate when the same subjects are involved in both conditions.
Let's say you want to conduct a hypothesis test to determine whether there is a significant difference in the mean distances thrown by children's dominant versus weaker hands. In this case, the researcher measures the same group of children twice, once using the dominant hand and once using the weaker hand. The dependent t-test would be appropriate here because it deals with paired samples or matched pairs within one group.
The null hypothesis (H0) for a dependent t-test typically states that there is no difference between the means of the two related groups. The alternative hypothesis (Ha) suggests that there is indeed a significant difference. When the assumptions of the dependent t-test are met, such as the data being approximately normally distributed and the pairs are chosen randomly and are independent of each other, you could use this statistical test to analyze your data.