Women diagnosed with breast cancer whose tumors have not spread may be faced with a decision between two surgical treatments— mastectomy (removal of the breast) or lumpectomy ( only the tumor is removed). In a long- term study of the effectiveness of these two treatments, 701 women with breast cancer were randomly assigned to one of two treatment groups. One group received mastectomies, and the other group received lumpectomies and radiation. Both groups were followed for 20 years after surgery. It was reported that there was no statistically significant difference in the proportion surviving for 20 years for the two treatments (Associated Press, October 17, 2002). Suppose that this conclusion was based on a 90% confidence interval for the difference in treatment proportions. Which of the following three statements is correct? Explain why you chose this statement.
Statement 1: Both endpoints of the confidence interval were negative.
Statement 2: The confidence interval included 0.
Statement 3: Both endpoints of the confidence interval were positive.