You are a researcher at UNCW who studies effective treatments for depression. Over the past few years, a treatment called "Building Healthy Relationships" has become Increasingly popular. The therapy was developed by researchers at Stanford University, and they have now shown in dozens of published articles with hundreds of patients that the treatment reduces symptoms of depression. In fact, on a depression scale ranging from 1 to 20, a score of 15 or above indicates depression. Following "Building Healthy Relationships," patients have an average score of 5 (SD = 4). You have carefully read the studies and notice a problem. All of the participants in the research have been women. Looking at the content of the program, it occurs to you that the treatment might be totally ineffective with men. You decide to test whether men receiving the "Building Healthy Relationships" curriculum will have higher depression scores following treatment than women. You administer the therapy to a depressed man. Following treatment, his depression score is 10. Following the steps for hypothesis testing, do man have greater depression following treatment than women do? a. Provide the null and alternative hypotheses using statistical notation. b. What are the characteristics of the comparison distribution? c. Use a conventional 5% level of significance. What is the cut-off Z-score? d. What is the Z-score for the man in your study? e. What is your conclusion?
