2. A sport physiologist is interested in the proportion of professional marathon runners who have very high hemoglobin counts. To this end, she randomly selects 50 marathon runners and measures their hemoglobin levels. She finds that the sample proportion with very high hemoglobin counts is 0.32. (a) Based on these data, compute a 90% two-sided confidence interval for the proportion of professional marathon runners with very high hemoglobin counts. State all assumptions and show all your work. (b) Compute a 90% lower confidence bound and a 90% upper confidence bound. State the associated one-sided confidence intervals (c) Find a 95% two-sided confidence interval for the proportion of professional marathon runners with very high hemoglobin counts. Why is your answer in (c) wider than in (a)? State all assumptions.