Answer the question below. Please ensure that you show the appropriate work, especially from the PANIC or State-Plan-Do-Conclude method.

The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal. Of these, 89 say "Yes."

a) Construct and interpret a 99% confidence interval for the proportion of all visitors to Yellowstone who favor the restrictions. (Use PANIC or State-Plan-Do-Conclude)

b) Based on your work in part "a)", can the U.S. Forest Service conclude that MORE THAN HALF of visitors to Yellowstone National Park favor the proposal? Justify your answer.