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.

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Let represent the probability that Joy Milne can correctly determine whether someone has Parkinson's disease from smelling their shirt. What is the value of if she is just guessing?

0.05

0.25

0.50

0.92

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Set up the correct null and alternative hypotheses in symbols to test this scenario.

H₀: p =<> 0.500.921112

H_a: p =<> 0.500.921112

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Use the One Proportion applet to generate the null distribution of the proportion of "successes." Which of the following is closest to the value of the standard deviation of your null distribution?

0.01

0.08

0.14

1.80

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Determine the standardized statistic for the observed sample proportion of "successes." (Round answer to 2 decimal places, e.g. 1.75.)

z = Type your answer here

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Based on the standardized statistic, what conclusion you would draw about the research conjecture that Milne has the ability to detect Parkinson's disease at a rate higher than 50%? Choose the best among the following statements.

Because the standardized statistic is larger than 2, we have evidence to claim that Joy Milne's probability of correctly determining whether someone has Parkinson's disease is greater than 0.50.

Because the standardized statistic is larger than 2, we have evidence to claim that it is plausible that Joy Milne's probability of correctly determining whether someone has Parkinson's disease is equal to 0.50.

Because the standardized statistic is not larger than 2, we have evidence to claim that Joy Milne's probability of correctly determining whether someone has Parkinson's disease is greater than 0.50.

Because the standardized statistic is not larger than 2, we have evidence to claim that it is plausible that Joy Milne's probability of correctly determining whether someone has Parkinson's disease is equal to 0.50.

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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?

Stronger evidence, because the standardized statistic is around 3.5 which is farther from 0 than the previous standardized statistic.

Stronger evidence, because the standardized statistic is around 6.2 which is farther from 0 than the previous standardized statistic.

Weaker evidence, because the standardized statistic is around 6.2 which is farther from 0 than the previous standardized statistic.

Weaker evidence, because the standardized statistic is around 3.5 which is farther from 0 than the previous standardized statistic.

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