National health insurance. An investigator at one of Japan’s 47 prefectures wants to know how many citizens are in the National Health Insurance system (Kokumin-

Kenkō-Hoken) or in the Employees’ Health Insurance system (Kenkō-Hoken). She chooses 17 citizens at random and finds that all 17 participate in the national system.

a) Check the assumptions and conditions for inference on proportions.

b) If conditions are met, find a 95% confidence interval for the true proportion of citizens participating in the National Health Insurance system. If conditions are not met, explain why.