Super Bowl: 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. Ratings for the 2019 Super Bowl between the New England Patriots and the Los Angeles Rams indicate that 41% of television sets in the United States were tuned to the game. Someone claims that the percentage of people who watched the game in this town was less than 41%. 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.