Although we know some animals, like dogs, have a keen sense of smell, what about humans? A woman from Scotland, Joy Milne, claimed that she was able to determine whether someone had Parkinson’s disease just based on their smell (Morgan, 2016). Her husband died from the disease and she noticed that he started smelling different prior to his diagnosis. To test this, researchers had six people known to have Parkinson’s disease and six people thought not to have the disease wear t-shirts for a day. They collected the shirts and then tested Milne. She correctly identified 11 of the 12 shirts. 

a. Suppose we let heads represent a correct guess and tails represent an incorrect guess. How many times would you need to flip a coin to model outcomes from someone just guessing whether a shirt came from a Parkinson’s patient on the test the researchers gave Joy Milne? 

b. Use the One Proportion applet to answer the question, “Is it unlikely that someone could identify at least 11 out of 12 shirts correctly if they were just guessing?” Explain how you determined your answer based on the results in the applet. 

c. Would you say that we have strong evidence that Joy Milne tends to do better than just guessing in picking which shirts come from someone with Parkinson’s disease? Explain your reasoning. 

d. Milne was adamant that one of the shirts came from someone with the disease when, in fact, that person had not been diagnosed. However, eight months later, the person Milne claimed had Parkinson’s was given a diagnosis that he had the disease. So in fact Milne got all 12 correct! Does this now give stronger or weaker evidence that she is doing better than just guessing compared to what you thought when answering part (c)? How are you deciding? 

e. How is your answer from part (d) related to the new location of the statistic in the simulated distribution in the applet?