Question

(2 pts) A noted psychic was tested for ESP. The psychic was presented with 180 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 43 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 180 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 Ha :p> .2 (a) What is the z-statistic for this test? (b) What is the P-value of the test?

Answer 1

We want to test hypothesis Ho : p-0.2 Ha p 0.2 This is an upper tailed test Nul Hypothesis, Ho :p 0.2 is also correct) (Alternative Hypothesis, also called Hi) X 43 n 180 Sample proportion, p= 0.238889, n-180 and claimed proportion, P 0.2 Significance level, α-0.05 (If no value is given, we take level of 0.05) now, calculating statistics P × (1-P) 0.2x (1-0.2) 180 Standard Deviation of p, σβ 0.0298 (43180)-0.2 0.0298 p-0.2 1.3043731.30 observed Test statistic,Z1.30 Since this is upper tailed test, p-value P(Z > Zobserved) P(Z1.30) P(Z< 1.30) 0.0968 p-value: 0.0968 Note that exact p-value for above test is: 0.0960532204 Rejection Criteria: Reject Ho if p-value< a Decision: Since 0.09680.05, we fail to reject the null hypothesis. There is insufficient evidence to conclude that p is greater than 0.2