Answer the question in Problem 9.50 using permutation test methods?

Cancer

Serum estradiol is an important risk factor for breast cancer in postmenopausal women. To better understand the etiology of breast cancer, serum-estradiol samples were collected from 25 premenopausal women (at about the same time period of the menstrual cycle) of whom 10 were Caucasian and 15 were African American. Data were collected on both serum estradiol as well as body mass index (BMI) = weight (kg)/height² (m²), which is an important measure of overall obesity. The data are shown in Table 9.16.

The distribution of serum estradiol is usually highly skewed (especially for premenopausal women), and we are reluctant to assume normality.

Table 9.16 Relationship of serum estradiol, BMI, and ethnicity in 25 premenopausal women

 

Serum estradiol Ethnic group" Estradiol rank ID (pg/mL) BMI 94 25 18.9 54 20 19.7 3 31 9.5 20.7 4 21 23.4 46 18 23.3 56 21 25.1 18 35.6 19 26.2 1 12 22.3 14 10 20.4 11 25 21.7 12 35 12 20.0 13 22 21.0 23 14 71 21.8 15 43 16 32.7 35 16 12 23.6 24.7 17 42 15 1 23.2 18 50 19 19 44 17 33.9 20 41 14 20.6 21 28 8. 24.7 22 65 22 26.3 20.1 23 31 9.5 24 35 12 22.5 25 91 24 29.1 *1 = Atrican-American, 0 = Caucasian.