Question

A noted psychic was tested for extrasensory perception. The psychic was presented with 2 0 0 cards face down and asked to determine if each card were one of five symbols: a star, a cross, a circle, a square, or three wavy lines. The psychic was correct in 5 0 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 2 0 0 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime. What do we know about the value of the P -value for the hypothesis test: Ha: p>0.20 ? ( Note: Use the large-sample z statistic. ) a. P-value < 0.01 0.02 < b. P-value < 0.03 0.03 < c. P-value < 0.04 0.05 < d. P-value < 0.10

Answer 1

C. P- value < 0.04 0.05

Explanation:

hello,

we were given the sample size, n = 200

also the probability that the psychic correctly identifies the symbol on the 200 card is

`p=(50)/(200)= 0.25`

using the large sample Z- statistic, we have

`Z=(p- 0.20)/(√(0.2(1-0.2)/200) )`

=
`(0.25-0.20)/(√(0.16/200))`

= 1.7678

thus the P - value for the hypothesis test is P(Z > 1.7678) = 0.039.

from the above, we conclude that the P- value < 0.04, 0.05