A poll reported that only 408 out of a total of 1549 adults in a particular region said they had a "great deal of confidence" or "quite a lot of confidence" in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met. Complete parts (a) through (d) below. a. Find a 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools, and interpret this interval. The 95% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is ( (Round to three decimal places as needed.) Interpret this interval. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals rounded to three decimal places as needed.) O A. We are O B. We are OC. There is a OD. There is a % confident that the every sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between | and % confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between and % chance that the sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between and % chance that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between | and b. Find an 80% confidence interval and interpret it. The 80% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is ( (Round to three decimal places as needed.) Interpret this interval. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals rounded to three decimal places as needed.) O A. There is a O B. There is a % chance that the sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between and % chance that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between | and OC. We are % confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between and O D. We are % confident that the every sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between and c. Find the width of each interval by subtracting the lower proportion from the upper proportion, and state which interval is wider. The width of the 95% confidence interval is (Round to three decimal places as needed.) and the width of the 80% confidence interval is The (1) interval is wider.