A researcher interested in treating chronic back pain recruited 20 adults diagnosed with the same back injury. Participants were matched on age, gender, time since injury, and level of back pain experienced. Half of the participants were randomly assigned to receive 8-weeks of a new type of physical therapy designed to increase strength around the injured part of the back. The other half of participants received a placebo pill and were told this was a "new drug" designed to reduce inflammation in the muscles of their back which should reduce their pain. At the end of 8 weeks, participants in both groups completed a pain level inventory that asked a variety of questions related to their current level of back pain.Higher scores on the inventory indicate a higher level of back pain. The data below reflect the inventory scores for participants in each group:

New Placebo Pill Physical Therapy 6 7 3 4 5 6 N A A 9 5 6 7 a. (3 points): What is the independent variable and what are the levels of the independent variable? b. (2 points): What is the dependent variable? c. (3 points): What is the null hypothesis for this study? Be sure you include the variables from the description above in your answer. d. (5 points): Using the correct function in Excel, conduct a statistical test of the null hypothesis at p = .05. Please make sure you write out your statistical conclusion in the correct format