During one semester of a healthy living class taught at Hope College, students were weighed (in kilograms), were weighed under water (in kilograms), and had their body fat percentage calculated. These were all done at the beginning of the semester and again at the end of the semester. We will consider this a representative sample of all students taking this class around this time. The data are available in Weight, WaterWeight, and BodyFat.
a. Complete three theory-based tests to determine whether or not Hope students’ weight, underwater weight, and body fat percentage are different at the end of the semester when compared to the beginning. Make sure validity conditions hold before conducting the test. When running the tests, find the mean difference, produce a dotplot of the diff erences, write out the hypotheses, determine the p-value, and write a conclusion.
b. If the result is significant, determine the direction of the change. Can you explain the differences in these directions?