The variation in the effects of dioxin could be due to variation in how well it binds to a steroid receptor-- this may vary widely from organism to organism with receptor sequence/shape. To test if an illness is related to dioxin, use control (untreated) and treated cells given dioxin and look for changes to appear only with dioxin administration. Telling if an individual was sick to dioxin would be much harder perhaps impossible since you could not have a control group and the illness was already in place, but you would have to look for dioxin-specific symptoms.
Work Step by Step
The key here is to review earlier material on receptors and to combine it with your new knowledge (this chapter) of protein sequence/function variation among organisms. Be sure to include control groups in any proposed experiments.