You see a story on the news about a Tarot-card reader who claims to be able to tell whether someone has cancer or not by 'reading the cards'. You, being a skeptic, decide to test this, and you send 100 people to visit the Tarot-card reader. 50 of these people have cancer but are not showing any obvious external signs of illness that would give it away ('sick' subjects); the other 50 people are normal and do not have any cancer or other health problems ('healthy' subjects).
a) Each subject is either sick or healthy, and each person gets diagnosed by the Tarot-card reader as positive or negative for cancer (i.e., positive patients are thought to have cancer by the Tarot-card reader). Using the language of signal detection theory, describe the labels that you would attach to each of the 4 possible outcomes of this 'experiment'. (10 points)
b) You are initially surprised when your research assistant brings you the results and shows you that the Tarot-card reader correctly identified 46 out of the 50 sick patients as being positive for cancer. Your assistant is excited and wants to publish this finding immediately. What should you do and why? Explain your logic carefully. (10 points)
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