The paper Sociochemosensory and Emotional Functions (Psychological Science [2009]: 11181124) describes an interesting experiment to determine if

The paper €œSociochemosensory and Emotional Functions€ (Psychological Science [2009]: 1118€“1124) describes an interesting experiment to determine if college students can identify their roommates by smell. Forty-four female college students participated as subjects in the experiment. Each subject was presented with a set of three t-shirts that were identical in appearance. Each of the three t-shirts had been slept in for at least 7 hours by a person who had not used any scented products (like scented deodorant, soap, or shampoo) for at least 48 hours prior to sleeping in the shirt. One of the three shirts had been worn by the subject€™s roommate. The subject was asked to identify the shirt worn by her roommate. This process was then repeated with another three shirts, and the number of times out of the two trials that the subject correctly identified the shirt worn by her roommate was recorded. The resulting data is given in the accompanying table.

a. Can a person identify her roommate by smell? If not, the data from the experiment should be consistent with what we would have expected to see if subjects were just guessing on each trial. That is, we would expect that the probability of selecting the correct shirt would be 1/3 on each of the two trials. It would then be reasonable to regard the number of correct identifications as a binomial variable with n = 2 and p = 1/3. Use this binomial distribution to compute the proportions of the time we would expect to see 0, 1, and 2 correct identifications if subjects are just guessing.
b. Use the three proportions computed in Part (a) to carry out a test to determine if the numbers of correct identifications by the students in this study are significantly different than what would have been expected by guessing. Use a = .05. (Note: One of the expected counts is just a bit less than 5. For purposes of this exercise, assume that it is OK to proceed with a goodness-of-fit test.)

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Number of Correct Identifications 0 2 Observed Count 21 10 13