Question: A survey of Americans and their TV viewing habits for this past year was done by a cable company. 287 people said that they find themselves watching more cable TV over this past year. While 268 people said that they did not find themselves watching more cable TV over this past year.

a. What would be the point estimate for the population proportion of Americans who would say that they find themselves watching more cable TV over this past year?

b. Find the 95% confidence interval for the population proportion of Americans who would say that they find themselves watching more cable TV over this past year.

c. The survey did not give information about the percentage of cable TV viewers who watch the premium channels on a daily basis. How many cable TV viewers should be in a sample to be 99% sure that the point estimate will be within 8.5 percentage points of the correct population percentage? (Remember to round up here)