A poll reported that only 502 out of a total of 1685 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 99% 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 99% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is ( D- (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 % 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. O B. 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 OC. 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 O D. There is a % 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 a 90% confidence interval and interpret it. % confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is ( H D- The 90 (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.) OA. 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 O B. There is a % 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 99% confidence interval is and the width of the 90% confidence interval is The interval is wider. (Round to three decimal places as needed.) d. How would a 95% interval compare with the others in width? O A. A95% interval would be wider than the 99% confidence interval but narrower than the 90% confidence because intervals get wider with increasing confidence level. OB. A95% interval would be wider than the 99% confidence interval but narrower than the 90% confidence because intervals get narrower with increasing confidence level. OC. A 95% interval would be narrower than the 99% confidence interval but wider than the 90% confidence because intervals get wider with increasing confidence level. O D. A 95% interval would be narrower than the 99% confidence interval but wider than the 90% confidence because intervals get narrower with increasing confidence level.