Time magazine (July 15, 2002) quoted a poll of 10,000 Americans in which only 4% said they

Question:

Time magazine (July 15, 2002) quoted a poll of 10,000 Americans in which only 4% said they were vegetarians.
a. What has to be assumed about this sample to construct a confidence interval for the population proportion of vegetarians?
b. Construct a 99% confidence interval for the population proportion. Explain why the interval is so narrow, even though the confidence level is high.
c. In interpreting this confidence interval, can you conclude that fewer than 10% of Americans are vegetarians? Explain your reasoning.