Suppose that you are interested in determining whether exposure to the organochloride DDT, which has been used extensively as an insecticide for many years, is associated with breast cancer in women. As part of a study that investigated this issue, blood was drawn from a sample of women diagnosed with breast cancer over a six-year period and a sample of healthy control subjects matched to the cancer patients on age, menopausal status, and date of blood donation. Each woman's blood level of DDE (an important byproduct of DDT in the human body) was measured, and the difference in levels for each patient and her matched control calculated. A sample of 171 such differences has mean \(\bar{d}=2.7 \mathrm{ng} / \mathrm{mL}\) and standard deviation \(s_{d}=15.9 \mathrm{ng} / \mathrm{mL}\). Differences were calculated as \(D D E_{\text {cancer }}-D D E_{\text {control }}\).

(a) Test the null hypothesis that the mean blood levels of DDE are identical for women with breast cancer and for healthy control subjects. What do you conclude?

(b) Would you expect a \(95 \%\) confidence interval for the true difference in population mean DDE levels to contain the value 0 ?