Which of Mill's Methods Is Illustrated in the Following Passage

Short Answer

Which of Mill's Methods is illustrated in the following passage? If, in your opinion, the conclusion reached indicates that an inadequate hypothesis was employed, explain why and formulate a better hypothesis.
After eating lunch at the same restaurant, five people became ill with food poisoning. Inspectors from the Health Department learned the following: Bill had chicken, potato salad, green beans, and tapioca pudding; Alice had the roast duck, tossed salad, asparagus with béarnaise sauce, and the tapioca pudding; Patricia had the beef wellington, Waldorf salad, tapioca pudding, and steamed broccoli; James had lamb, tzadziki, ouzo, and tapioca pudding; and Peter had scallops, a tossed salad, steamed broccoli, and the tapioca pudding. The inspectors concluded that since they all had the tapioca pudding for dessert, it was what caused the outbreak of botulism (food poisoning).