The authors of the article “Adjuvant Radiotherapy and Chemotherapy in Node- Positive Premenopausal Women with Breast Cancer” (New Engl. J. Med. 1997: 956–962) reported on the results of an experiment designed to compare treating cancer patients with only chemotherapy to treatment with a combination of chemotherapy and radiation. Of the 154 individuals who received the chemotherapy-only treatment, 76 survived at least 15 years, whereas 98 of the 164 patients who received the hybrid treatment survived at least that long.

a. With p₁ denoting the proportion of all such women who, when treated with just chemotherapy, survive at least 15 years and p₂ denoting the analogous proportion for the hybrid treatment, calculate a 99% CI for p₁ – p₂.

b. Based on the interval from part (a), can either treatment be judged superior to the other? Why or why not?