Some people believe that wearing copper bracelets can help decrease the symptoms of arthritis in the hands. A doctor decides to test this theory by randomly assigning 100 of her patients with arthritis of the hand to wear a copper bracelet for three months, 100 to wear a nickel bracelet for three months, and the remaining 79 to wear no bracelet for three months. After three months, she finds that the average pain rating in the first group has decreased 1.5 pts (on a scale of 1 to 10) as opposed to a decrease of 0.3 points in the second group and no change in the third group. (a) Is this an observational study or a controlled experiment? Explain. (b) Can the researcher conclude that wearing a copper bracelet causes a decrease in symptoms of arthritis? Explain. (c) Identify the four steps of this statistical investigation. 1. Ask a question that can be answered by collecting data 2. Decide the plan to collect data for the study. (Identify the subjects and the outcome variables.) Are the outcome variables numerical or categorical? 3. Summarize and analyze the data. 4. Draw a conclusion and communicate the results.