Question

4. A noted psychic was tested for extrasensory perception (ESP). The psychic was presented with 400 cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, or square. The psychic was correct in 120 cases. Let ? represent the probability that the psychic correctly identifies the symbols on the cards in a random trial. Suppose you wish to see if there is evidence that the psychic was doing better than just guessing. To make this determination, you test the hypotheses ?0:?=0.25 versus ??:?>0.25 . The ? value of your test is:

a. 0.0146

b. 0.9896

c. 0.0104

5. The standard deviation of the sampling distribution for the sample proportion is:

A. ?

B. ?(1−?)?‾‾‾‾‾‾√

C. ?̂

D. ?̂(1−?̂)?‾‾‾‾‾‾√

Answer 1

Answer 4

We know that the assumed population proportion, p is 0.25.

The sample proportion, p_hat is 120/400= 0.3.

Sample size, n= 400.

We know that the

null hypothesis, H0: p<=0.25

alternate hypothesis, Ha: p>0.25

Thus, this is a one tailed test.

The test statistic= (p_hat-p)/sqrt(p(1-p)/n)

= (0.3-0.25)/sqrt(0.25*0.75/400)

= (0.05)/0.02165064

= 2.309401 ~ 2.31

Thus, the p_value of this test (as can be seen from the z distribution table) is 0.01044.

Answer 5

The correct answer is B. sqrt(p*(1-p)/n)

This is the same equation we used to calculate the test statistic.