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 or not someone had Parkinson’s disease just based on their smell (Morgan, J., 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. Let π represent the probability that Joy Milne can correctly determine whether someone has Parkinson’s disease from smelling their shirt. What is the value of π if she is just guessing? 

b. State the null hypothesis and the alternative hypothesis in symbols to test this scenario. 

c. Use the One Proportion applet to generate the null distribution of the proportion of “successes.” What is the value of the standard deviation of your null distribution? 

d. Determine the standardized statistic for the observed sample proportion of “successes.” 

e. Based on the standardized statistic, state the conclusion you would draw about the research conjecture that Milne has the ability to detect Parkinson’s disease at a rate higher than 50%. 

f. 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 she claimed had Parkinson’s was given a diagnosis that he had the disease. So she, in fact, got all 12 correct! Using this new statistic of 12 out of 12, determine the standardized statistic for the observed sample proportion of “successes.” Does this now give stronger or weaker evidence that she is doing better than just guessing than if she only got 11 out of 12 correct like what was originally thought?