A psychologist measures stress levels on a standardized scale in $8$ patients before and after a mindfulness intervention. The results are:

Using the sign test or the Wilcoxon signed-ranks test, we can test for no difference between the stress levels before and after the mindfulness intervention. How does the Wilcoxon signed-ranks test differ from the sign test in terms of information used?

A researcher collects paired data with $36$ nonzero differences. Assuming the population of matched pairs has differences with a median of $0$, Let T denote the sum of positive signed ranks. What is the expected value of T?

A study investigates whether there is a significant difference in cholesterol levels of patients before and after a new diet program. The cholesterol levels in milligrams per deciliter of $8$ patients are measured at the start and after $6$ months. Data pairs are as follows:

Analyze the data using the rank correlation coefficient. What does the result suggest about the claim that the diet program is associated with a consistent pattern of change in cholesterol levels?