If we have learned to solve problems by one method, we often have difficulty bringing new insight to similar problems. However, electrical stimulation of the brain appears to help subjects come up with fresh insight. In a recent experiment conducted at the University of Sydney in Australia, 40 participants were trained to solve problems in a certain way and then asked to solve an unfamiliar problem that required fresh insight. Half of the participants were randomly assigned to receive non-invasive electrical stimulation of the brain while the other half (control group) received sham stimulation as a placebo. The participants did not know which group they were in. In the control group, 20% of the participants successfully solved the problem while 60% of the participants who received brain stimulation solved the problem.

(a) Is this an experiment or an observational study? Explain.

(b) From the description, does it appear that the study is double-blind, single-blind, or not blind?

(c) What are the variables? Indicate whether each is categorical or quantitative.

(d) Make a two-way table of the data.

(e) What percent of the people who correctly solved the problem had the electrical stimulation?

(f) Give values for p̂_E, the proportion of people in the electrical stimulation group to solve the problem, and p̂_S, the proportion of people in the sham stimulation group to solve the problem. What is the difference in proportions p̂_E − p̂_S?

(g) Does electrical stimulation of the brain appear to help insight?