Final answer:
The correct answer is option a. The appropriate inferential statistic for comparing the performance of the same group of children under two conditions (wearing weighted and unweighted vests) is a dependent sample t-test, as the samples are dependent or paired.
Step-by-step explanation:
In the context of the provided study, where children wore either a weighted vest or an unweighted vest, the inferential statistic that should be used to compare the difference between the two conditions is a dependent sample t-test. This is because the same group of children is being tested under two different conditions, making the samples dependent or paired. The dependent sample t-test is appropriate here rather than an independent sample t-test, as the latter is used for comparing two different groups of subjects.
An independent sample t-test is used when comparing two groups that are separate from one another and have no pairing or dependency, such as the case where a powder diet is tested on one group and a liquid diet on another.
A repeated measures ANOVA is similar to the dependent sample t-test in the sense that it involves dependent samples or repeated measures on the same subjects. However, it extends to more than two conditions or time points, which goes beyond the scenario outlined in the study question with just two conditions.
One-way ANOVA is utilized when there are more than two groups to compare and the samples are independent; this test checks if there are statistically significant differences among group means. In our case with only two conditions and the same subjects, one-way ANOVA is not the appropriate test. Moreover, since we are not testing more than two different diets or conditions, the use of ANOVA is not warranted. Therefore, the correct option for the inferential statistic to use is a dependent sample t-test.