Question: A physician claims that as soon as his patients have a positive pregnancy test, he is generally able to predict the sex of the baby and that his probability of being right is greater than the one-half that would be expected if he were just guessing. A skeptic challenges his claim, and the physician decides to collect data for the next ten pregnancies to try to support his claim.
a. From the perspective of the physician, what are the null and alternative hypotheses for this situation?
b. Out of the ten pregnancies, he is correct six times. Write in words what probability needs to be computed to find the p-value.
c. The p-value for this test is .377. Does that prove that the skeptic is correct? Explain.
d. State the appropriate conclusion, using a = .05.
e. Assuming that the physician really does have some ability to make these predictions, what would you recommend that he do to increase the likelihood that he can convince the skeptic?