Chapter 13.4, Problem 11E

It is believed that women in the postmenopausal phase of life suffer from calcium deficiency. This phenomenon is associated with the relatively high proportion of bone fractures for women in that age group. Is this calcium deficiency associated with an estrogen deficiency, a condition that occurs after menopause? To investigate this theory, L. S. Richelson and colleagues³ compared the bone mineral density in three groups of women.

The first group of 14women had undergone oophorectomy (the surgical removing of ovaries) during young adult womanhood and had lived for a period of 15 to 25 years with an estrogen deficiency. A second group, identified as premenopausal, were approximately the same age (approximately 50 years) as the oophorectomy group except that the women had never suffered a period of estrogen deficiency. The third group of 14 women were postmenopausal and had suffered an estrogen deficiency for an average of 20 years. The mean and standard error of the mean for the three samples of lumbar spine bone-density measurements—14 measurements in each sample, one for each subject—are recorded in the following table.

a Is there sufficient evidence to permit us to conclude that the mean bone-density measurements differ for the three groups of women? What is the p-value associated with your test?

b What would you conclude at the α = .05 level?