"Hospital Chiefs Wary of Mandate on Error Reports" states that "many hospital administrators are leery of the push toward mandatory reporting of medical errors."17 Specifically, in a survey conducted between 2002 and 2003, a certain proportion of chief executives and operating officers in various states said that a state-run, mandatory, nonconfidential reporting system would encourage lawsuits, despite evidence that patients are less likely to sue if doctors admit their mistakes and apologize. Based on the observed sample proportion, a 95% confidence interval for the proportion of all hospital administrators who believe such a system would encourage lawsuits is (0.67, 0.91).

a. Would a 90% confidence interval be wider or narrower?

b. The point estimate for population proportion must be at the center of the reported interval. What is it?

c. What is the margin of error in this estimate?

d. What is the approximate standard deviation of the sample proportion?

e. Tell which one of these is the correct interpretation of the interval (0.67, 0.91):

1. The probability is 0.95 that the population proportion falls in this interval.

2. The probability is 0.95 that the sample proportion falls in this interval.

3. We are 95% sure that the population proportion falls in this interval.

4. We are 95% sure that the sample proportion falls in this interval.

f. Suppose 75 executives and officers were surveyed. Is our formula for approximate standard deviation accurate if we want to draw conclusions about a population of several thousand executives and officers?