What test can be used to compare the mean of the two groups?

Cancer

Age at menarche (onset of menstrual periods) is an important risk factor for breast cancer and possibly ovarian cancer. In general, women who reach menarche at an earlier age have a higher incidence of breast cancer. The long-term trend in developed countries is that age at menarche

has been declining over the past 50 years. One hypothesis is that women with higher childhood SES have an earlier age at menarche.

Suppose we identify 20 girls with low childhood SES (that is, head of household is a blue-collar worker) and find mean age at menarche of 13.4 years with a standard deviation of 1.4 years. We identify an additional 30 girls with high childhood SES (head of household is a white-collar worker or executive) and find a mean age at menarche of 12.9 years with a standard deviation of 1.5 years. Assume that the underlying variance of age at menarche for girls with low childhood SES and girls with high childhood SES is the same.