Question

Do doctors in managed-care plans give less charity care? Researchers chose 60 communities at random and then chose doctors at random in each community. In all, they interviewed 10,881 doctors. Overall, 77.3 percent of the doctors said they had given some care free or at reduced rates because of the patient's financial need in the month before the interview. Doctors who received at least 85 percent of their practice income from managed-care plans were significantly less likely than other doctors to provide charity care.

For a simple random sample of size 10,881, the margin of error for 95 percent confidence is about:
a.± 9.6%.
b.± 3%.
c.± 0.0096%.
d.± 0.96%.

Answer 1

To determine the margin of error for a 95% confidence interval with a sample size of 10,881, computations involving the sample proportion and the z-score are necessary. However, since the question provides possible margins of error, the most logical selection is ± 0.96%.

Step-by-step explanation:

The question you're asking relates to determining the margin of error for a 95% confidence interval given a simple random sample of size 10,881. The margin of error can be calculated using the formula for the margin of error at a specified confidence level, which is M = z * sqrt(p(1-p)/n), where M is the margin of error, z is the z-score corresponding to the desired confidence level, p is the sample proportion, and n is the sample size.

In this instance, we're not given the sample proportion p or the actual z-score to use, which implies that the researchers have already calculated these values and are presenting us with a range of possible margins of error for the 95% confidence interval. Based on such large sample size, the margin of error will be small, and since we're discussing a confidence interval, the reasonable selection among the given choices is d. ± 0.96%.