54. An Employee Benefits Research Institute survey of 1250 workers over the age of 25 collected opinions on the health care system in America and on retirement planning (AARP Bulletin, January 2007).

a. The American health care system was rated as poor by 388 of the respondents. Construct a 95% confidence interval for the proportion of workers over 25 who rate the American health care system as poor.

b. Eighty-two percent of the respondents reported being confident of having enough money to meet basic retirement expenses. Construct a 95% confidence interval for the proportion of workers who are confident of having enough money to meet basic retirement expenses.

c. Compare the margin of error in part

(a) to the margin of error in part (b). The sample size is 1250 in both cases, but the margin of error is different. Explain why.