1. A noted psychic was tested for ESP. The psychic was presented with 200 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 49 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 200 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
H0:p=.2
Ha:p>.2
(a) What is the z-statistic for this test?
(b) What is the P-value of the test?
2. A survey of 1305 people who took trips revealed that 96 of them included a visit to a theme park. Based on those survey results, a management consultant claims that less than 8 % of trips include a theme park visit. Test this claim using the ?=0.01significance level.
(a) The test statistic is:
(b) The P-value is: