Suppose that you are interested in determining whether exposure to the organochl

Question

Suppose that you are interested in determining whether exposure to the organochlorine 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 from 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 d^bar = 2.7 ng/ml and standard deviation s_d = 15.9 ng/ml [11]. (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? Explain.

Explanation / Answer

(a) Null Hypothesis : H0 : Mean blood levels of DDE are identical for women with breast cancer and for health control subjects. DDE - non-DDE = 0

Alternative Hypothesis : Ha : Mean blood levels of DDE are Higher for women with breast cancer and for health control subjects. DDE - non-DDE >0

Test Statistic

Here dbar = 2.7 ng/ml

sd = 15.9 ng/ml

Z = (dbar )/ (sd / sqrt(n) = 2.7 / ( 15.9/ sqrt (171)) = 2.7/ 1.2159 = 2.20

the critical value of Z for 95% confidience interval 95% is = + 1.96

so here Z > Zcr so we shall reject the null hypothesis and can conclude that there Mean blood levels of DDE are not same for Women with cancer with respect to the control subjects.

(b) 95% Confidence interval = dbar +- Z95% (sd /sqrt(n) )

= 2.7 +- 1.96 * (15.9/ sqrt (171))

= (0.317, 5.083)

The confidence interval doesn't consist the true difference in population mean DDE levels value of 0 so we cansay that there is a difference between Mean DDE level between Breast - Cancer women and the other control subjects.

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