Nast Problen Problem List (1 point) A noted psychic was tested for ESP The psych

Question

Nast Problen Problem List (1 point) A noted psychic was tested for ESP The psychic was presented with 260 cards face down and was asked to determine if the card was one of 5 symbols: a star, cross, circle, square, or three wavy lines. The psychic was correct in 70 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 260 trials can be treated as an SRS from the population of all guesses. To see if there is evidence that the psychic is doing better than just guessing, we test Ho:p=.2 (a) What is the z-statistic for this test? (b) What is the P-value of the test?

Explanation / Answer

Solution:

Given that x = 70, n = 260
p = x/n = 70/260 = 7/26 = 0.2692

standard deviation sd = sqrt[p *(1-p)/n] = sqrt[ (0.2692* (1-0.2692))/260]

= 0.0275

Z-statistic = p - 0.2/sd = 0.2692- 0.2/0.02750

= 2.5164

P-value = 0.0059

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