High levels of blood sugar are associated with an increased risk of type 2 diabetes. A level higher than normal is referred to as “impaired fasting glucose.” The article “Association of Low-Moderate Arsenic Exposure and Arsenic Metabolism with Incident Diabetes and Insulin Resistance in the Strong Heart Family Study” reports a study in which 47 of 155 people with impaired fasting glucose had type 2 diabetes. Consider this to be a simple random sample.
a. Find a 95% confidence interval for the proportion of people with impaired fasting glucose who have type 2 diabetes.
b. Find a 99% confidence interval for the proportion of people with impaired fasting glucose who have type 2 diabetes.
c. A doctor claims that less than 35% of people with impaired fasting glucose have type 2 diabetes. With what level of confidence can this claim be made?
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