Examples 1, 3, and 5 referred to a study about astrology. Another part of the study used the following experiment: Professional astrologers prepared horoscopes for 83 adults. Each adult was shown three horoscopes, one of which was the one an astrologer prepared for them and the other two were randomly chosen from ones prepared for other subjects in the study. Each adult had to guess which of the three was theirs. Of the 83 subjects, 28 guessed correctly.
a. Defining notation, set up hypotheses to test that the probability of a correct prediction is 1/3 against the astrologers’ claim that it exceeds 1/3.
b. Show that the sample proportion = 0.337, the standard error of the sample proportion for the test is 0.052, and the test statistic is z = 0.08.
c. Find the P-value. Would you conclude that people are more likely to select their horoscope than if they were randomly guessing, or are results consistent with random guessing?