2.Professional astrologers prepared horoscopes for 83 adults. Each adult was sho

Question

2.Professional astrologers prepared horoscopes for 83 adults. Each adult was shown three horoscopes, one of which was the one the astrologer prepared for him or her 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 his or hers. Of the 83 subjects, 28 guessed correctly.

a.Define the parameter of interest and set up the 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?

Explanation / Answer

a)
p = 1/3 = 0.333 , n = 83
Null hypothesis : p = 0.333
alternative hypothesis : p > 0.333

b)Test statistic:

p bar = 28 / 83 = 0.337
standard error for proportion = sqrt ( p ( 1 -p) / n)

= sqrt ( 0.333 * 0.667 / 83) = 0.052

z = (pbar - p)/ SE
= ( 0.337 -0.333) / 0.052
= 0.08

c)
P value is calculated using z = 0.08 at 0.05 significance level
p value = 0.4681
As p value is greater than 0.05 so we fail to reject the null hypothesis.

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