The article “Doctors Cite Burnout in Mistakes” (San Luis Obispo Tribune, March 5, 2002) reported that many doctors who are completing their residency have financial struggles that could interfere with training. In a sample of 115 residents, 38 reported that they worked moonlighting jobs and 22 reported a credit card debt of more than $3000. Suppose that it is reasonable to consider this sample of 115 as a random sample of all medical residents in the United States.
a. Construct and interpret a 95% confidence interval for the proportion of U.S. medical residents who work moonlighting jobs.
b. Construct and interpret a 90% confidence interval for the proportion of U.S. medical residents who have a credit card debt of more than $3000.
c. Give two reasons why the confidence interval in Part (a) is wider than the confidence interval in Part (b).