You are the new head of HR of a $44 billion per year not for profit called the University of California. Part of your job is to develop health insurance plans for staff and faculty in the system (student health plans are an entirely different matter). You realize that the medical schools in the system are some of the best in the world and have developed a possible health insurance plan that is slightly higher cost than current plans, but guarantees employees access to the UC hospital system. You run a pilot where you offer this plan to 5,000 randomly selected employees during open enrollment. 1,250 of the employees sign up for the pilot. Please carry five decimals for all calculations. 1. Calculate a 95% Confidence Interval for the true share of the population that would pick up the plan if it were offered to everyone