A 2017 survey of U.S. adults found the 64% believed that freedom of news organization to criticize political leaders is essential to maintaining a strong democracy. Assume the sample size was 500.

a. How many people in the sample felt this way?

b. Is the sample large enough to apply the Central Limit Theorem? Explain. Assume all other conditions are met.

c. Find a 95% confidence interval for the proportion of U.S. adults who believe that freedom of news organizations to criticize political leaders is essential to maintaining a strong democracy.

d. Find the width of the 95% confidence interval. Round your answer to the nearest whole percent.

e. Now assume the sample size was increased to 4500 and the percentage was still 64%. Find a 95% confidence interval and report the width of the interval.

f. What happened to the width of the confidence interval when the sample size was increased. Did it increase or decrease?