In a study investigating the role of the organochlorine DDT in breast cancer, bl
ID: 3232210 • Letter: I
Question
In a study investigating the role of the organochlorine DDT in breast cancer, blood was drawn from a sample of women diagnosed with breast cancer and from healthy control subjects matched to the cancer patients with respect to age and menopausal status. Each subject's blood DDT-levels were estimated, and the differences in blood DDT between patients and their matched controls were calculated. A sample of 171 such differences has a mean d = 2.7 ng/ml and a standard deviation sd = 15.9 ml. a) Test the null hypothesis that that the mean blood levels of DDT are identical for the patients and the control subjects. What is your conclusion? b) What is the risk for a type 1 error in this test? c) Would you expect a 95 percent confidence interval for the true difference in population mean DDT levels to contain the value 0? Explain.Explanation / Answer
a) H0 : d = 0
Ha : d 0
= 0.05
degree of freedom, df = 171 - 1 = 170,
test statitstic, t = (x - µ)//sqrt(n) = (2.7 - 0)/(15.9/sqrt(171)) = 2.220571
p-value = 0.0277
this difference is considered to be statistically significant. There is sufficient evidence to suggest that the differences in blood DDT between patients and their matched controls is not equal to 0 and therefore the null hypothesis is rejected.
b) The risk for type 1 error is the significance level chosen, = 0.05
c) Since at = 0.05, the result was significant in part a, 0 will not appear in the 95% CI. This further proves that the difference is not equal to zero.