You plan to run an experiment on the use of helmets. People in the control group (C) get no incentives. People in the treatment group (T) receive $5 if they wear a helmet. Assume that the baseline rate is pc = .6 (i.e., 60% of people in Control wears a helmet). Your sample size of the treatment group is 10. Use a significance level of 5% and a one- sided test. a. How many of the 10 people in the treatment group do you expect to wear a helmet if there is no treatment effect? b. Suppose you observe 7 people wearing a helmet in your treatment group. What is the probability of observing at least 7 people wearing a helmet in the treatment group if there is no treatment effect? c. Repeat the above question for the following outcomes: 8, 9, and 10. Probability outcome is at least 8: Probability outcome is at least 9: Probability outcome is at least 10: d. For each of the following outcomes, determine if the outcome is significant at the 5% level: 7, 8, 9, and 10. Outcome 7: Outcome 8: Outcome 9: Outcome 10: e. Assume you expect that the intervention is effective, and that it increases the percentage of people wearing a helmet to 80%. For each of the following outcomes, calculate the probability of observing that exact outcome when the percentage of people wearing a helmet is 80%: 7, 8, 9, 10. Probability of getting exactly 7: Probability of getting exactly 8: Probability of getting exactly 9: Probability of getting exactly 10: f. Calculate the statistical power when the percentage of people wearing a helmet is 80%. g. Repeat the above steps for a sample size of 20 in the treatment group (focus on outcomes 15 and higher instead of 7 and higher). What happens to the statistical power?