There has been a considerable underfunding of the national Highway Trust Fund over the last 20 years, which has resulted in a dramatic decline in the maintenance of the nation’s roads and bridges. An organization representing highway construction companies is planning a nation-wide survey to estimate the proportion π of people who would support an increase in the gasoline tax. How large a sample is needed to obtain an estimate of π to within .02 using a 99% confidence interval. Consider two separate situations:
a. Suppose the organization has no idea of the value of π.
b. Suppose the organization is fairly certain the value of π is greater than 75%.