Agent Orange, the code name for a herbicide developed for the U.S. armed forces in the 1960s,

Question:

Agent Orange, the code name for a herbicide developed for the U.S. armed forces in the 1960s, was found to be extremely contaminated with TCDD, or dioxin. During the Vietnam War, an estimated 19 million gallons of Agent Orange was used to destroy the dense plant and tree cover of the Asian jungle. As a result of this exposure, many Vietnam veterans have dangerously high levels of TCDD in their blood and adipose (fatty) tissue. A study published in Chemosphere (Vol. 20, 1990) reported on the TCDD levels of 20 Massachusetts Vietnam vets who were possibly exposed to Agent Orange. The TCDD amounts (measured in parts per trillion) in both plasma and fat tissue of the 20 vets are listed in the accompanying table (left column).

a. Medical researchers consider a TCDD level of 3 parts per trillion (ppt) to be dangerously high. Do the data provide evidence (at α = .05) to indicate that the median level of TCDD in the fat tissue of Vietnam vets exceeds 3 ppt?

b. Repeat part a for plasma.

c. Medical researchers also are interested in comparing the TCDD levels in fat tissue and plasma for Vietnam veterans. Specifically, they want to determine whether the distribution of TCDD levels in fat is shifted above or below the distribution of TCDD levels in plasma. Conduct this analysis (at α = .05) and make the appropriate inference.

d. Find the rank correlation between the TCDD level in fat tissue and the TCDD level in plasma. Is there sufficient evidence (at α = .05) of a positive association between the two TCDD measures?