Question

A psychic claims to be able to predict the outcome of coin flips before they happen. Someone who guesses randomly will predict about half of coin flips correctly. In 100 flips, the psychic correctly predicts 57 flips. Do the results of this test indicate that the psychic does better than random guessing? The hypotheses are Ho:p=0.50 Ha:p>50 where p is the proportion of correct coin flip predictions by the psychic.

1. Give the test statistic for this problem.

Group of answer choices

a.Z = 1.40

b.Z = -9.43

c.Z = -1.40

2. What is the P value

a P-value = 0.2843

b P-value = 0.919

c P-value = 0.081

d P-value = 0.162

3. Give the conclusion based on the P-value above. Use a 5% level of significance.

a. Someone who guesses randomly will predict about half of coin flips correctly (about 50 out of 100). In 100 flips, the psychic correctly predicts 57 flips, a 14% increase. Therefore we can conclude that the psychic's predictions are not due to random chance.

b The psychic correctly predicted 57% of the coin flips (57 out of 100). A person who guesses randomly will correctly predict about 50% (half) of the 100 coin flips. So the psychic's predictions are significantly better.

c The psychic’s prediction of the outcomes of coin flips is not significantly better than we would expect with random guessing.

Answer 1

Solution:

Given: A psychic claims to be able to predict the outcome of coin flips before they happen.

n = 100

x = 57

The hypotheses are:

Ho:p=0.50 Vs Ha:p>50

p is the proportion of correct coin flip predictions by the psychic.

Part 1) the test statistic

where

thus

Part 2. What is the P value

For right tailed test , p-value is:

p-value = P(Z > z test statistic)

p-value = P(Z > 1.40 )

p-value = 1 - P(Z < 1.40 )

Look in z table for z = 1.4 and 0.00 and find corresponding area.

P( Z < 1.40) = 0.9192

thus

p-value = 1 - P(Z < 1.40 )

p-value = 1 -0.9192

p-value = 0.0808

p-value = 0.081

thus correct answer is:

C. P-value = 0.081

Part 3) Give the conclusion based on the P-value above. Use a 5% level of significance.

Since p-value = 0.081 > 0.05 level of significance,we fail to reject H0.

Thus correct answer is:

C. The psychic’s prediction of the outcomes of coin flips is not significantly better than we would expect with random guessing.