A simple random sample of 140 residents in a certain town was polled the week after the Super Bowl, and 75 of them said they had watched the game on television.
a. Construct a 95% confidence interval for the proportion of people in the town who watched the Super Bowl on television.
b. The 2013 Super Bowl between the Baltimore Ravens and the San Francisco 49ers was the third most watched television program in history, with 48.1% of television sets in the U. S. tuned to the game. Someone claims that the percentage of people who watched the game in this town was less than 48.1%. Does the confidence interval contradict this claim? Explain.
c. Use the results from the sample of 140 to estimate the sample size necessary for a 95% confidence interval to have a margin of error of 0.025.