Researchers conducted a study of 18 patients whose depression had not responded to treatment (Zarate, 2006). Half received one intravenous dose of ketamine, a hypothesized quick fix for depression; half received one intravenous dose of placebo. Far more of the patients who received ketamine improved, as measured by the Hamilton Depression Rating Scale, usually in less than 2 hours, than patients on placebo. 

a. What is the population of interest, and what is the sample in this study? 

b. Was random selection likely used? Explain your answer. 

c. Was random assignment likely used? Explain your answer.

d. What is the independent variable and what are its levels? What is the dependent variable? 

e. What is the null hypothesis and what is the research hypothesis?

f. What decision did the researchers make? (Respond using the language of inferential statistics.) 

g. If the researchers were incorrect in their decision, what kind of error did they make? Explain your answer. 

What are the consequences of this type of error, both in general and in this situation?