The Centers for Disease Control and Prevention

(CDCP) in Atlanta, Georgia, conducts an annual survey of the general health of the US. population as part of its Behavioral Risk Factor Surveillance System (New York Times, Mar. 29, 1995). Using random-digit dialing, the CDCP telephones US. citizens over 18 years of age and asks them the following four questions:

(1) Is your health generally excellent, very good, good, fair, or poor?

(2) How many days during the previous 30 days was your physical health not good because of injury or illness?

(3) How many days during the previous 30 days was your mental health not good because of stress, depression, or emotional problems?
(4) How many days during the previous 30 days did your physical or mental health prevent you from performing your usual activities?
Identify the parameter of interest for each question.
5-55 Refer to Exercise 5.54. According to the CDCP, 89,582 of 102,263 adults interviewed stated their health was good, very good, or excellent.

a. Use a 99% confidence interval to estimate the true proportion of US. adults who believe their health to be good to excellent. Interpret the interval.

b. Why might the estimate, part

a, be overly optimistic (i.e., biased high)?
j.j6 Substance abuse problems are widespread at New Jersey businesses, according to the Governor's Council for a Drug Free Workplace Report (SpringISummer 1995). A questionnaire on the issue was mailed to all New Jersey businesses that were members of the Governor's Council. Of the 72 companies that responded to the survey, 50 admitted that they had employees whose performance was affected by drugs or alcohol.

a. Use a 95% confidence interval to estimate the proportion of all New Jersey companies with substance abuse problems.

b. What assumptions are necessary to ensure the validity of the confidence interval?

c. Interpret the interval in the context of the problem.

d. In interpreting the confidence interval, what does it mean to say you are "95% confident"?

e. Would you use the interval of part a to estimate the proportion of all U.S. companies with substance abuse problems? Why or why not?