A public opinion polling agency plans to conduct a national survey to determine the proportion of

Question:

A public opinion polling agency plans to conduct a national survey to determine the proportion π of people who would be willing to pay a higher per kilowatt hour fee for their electricity provided the electricity was generated using ecologically friendly methods such as solar, wind, or nuclear. How many people must be included in the poll to estimate the population proportion within .04 of the population value using a 95% confidence interval. Consider two separate situations:
a. Suppose the polling agency has no previous information about the population proportion.
b. Suppose the polling agency is fairly certain that the population proportion is less than 30%.
c. Why are the sample sizes so different for the two situations?