11.66 In a study of a proposed treatment for diabetes prevention, 339 people under the age of 20 who were thought to be at high risk of developing type I diabetes were assigned at random to two groups. One group received twice-daily injections of a low dose of insulin. The other group (the control) did not receive any insulin, but was closely monitored. Summary data (from the article “Diabetes Theory Fails Test,” USA Today, June 25, 2001) follow.

Group n Number Developing Diabetes Insulin 169 25 Control 170 24

a. Use the given data to construct a 90% confidence interval for the difference in the proportion that develop diabetes for the control group and the insulin group.

b. Give an interpretation of the confidence interval and the associated confidence level.

c. Based on your interval from Part (a), write a few sentences commenting on the effectiveness of the proposed prevention treatment.